longitudinal waves travel in which medium

Longitudinal Waves

Mechanical waves are classified as longitudinal waves and transverse waves. Some examples of longitudinal waves are sound waves, seismic P-waves, and ultrasound waves. Transverse waves examples include electromagnetic waves and ocean waves. In this article, we will learn what is a longitudinal wave and its characteristics.

What Is Longitudinal Wave?

Longitudinal waves are waves where the displacement of the medium is in the same direction as the direction of the travelling wave.

The distance between the centres of two consecutive regions of compression or the rarefaction is defined by wavelength, λ. When the compression and rarefaction regions of two waves coincide with each other, it is known as constructive interference and if the regions of compression and rarefaction do not coincide, it is known as destructive interference.

Compression in a longitudinal wave is a region where the particles are the closest together while rarefaction in a longitudinal wave is a region where the particles are spread out.

Similar Reading: Transverse Waves

Longitudinal Wave Formula

• y is the displacement of the point on the travelling sound wave
• x is the distance the point travelled from the wave’s source
• t is the time elapsed
• y 0  is the amplitude of the oscillations
• c is the speed of the wave
• ω is the angular frequency of the wave

Quantity x/c = time ( wave takes to travel the distance x).

The frequency (f) of the wave is given by the formula: f=ω2π Hope you have understood what is a longitudinal wave along with its formula. Let us now learn about sound waves and pressure waves in detail.

Sound Waves

A sound wave is an example of a longitudinal wave and is produced by the vibrating motion of the particles that travel through a conductive medium. An example of sound waves in a longitudinal direction is the tuning fork.

In Sound waves, the amplitude of the wave is the difference between the maximum pressure caused by the wave and the pressure of the undisturbed air. The propagation speed of sound depends upon the type, composition of the medium, and temperature through which it propagates.

Pressure Waves

The pressure wave is defined as the propagation of disturbance in a medium as the pressure varies.

A harmonic pressure wave oscillation will be,

• y 0  is the amplitude of displacement
• k is the wavenumber
• x is the distance along the axis of propagation
• ω is the angular frequency
• t is the time
• φ is the phase difference

Characteristics of Longitudinal Waves

Compression.

In a longitudinal wave, compression is a region in which the particles of the wave are closest to each other.

Rarefaction

Rarefaction in a longitudinal wave takes place when the particles are farthest apart from each other.

The distance between two consecutive points in a longitudinal wave is known as wavelength. These consecutive points can be between two compressions or between two rarefactions.

Amplitude is the maximum displacement of the particle from its rest point. In a longitudinal wave, the distance from the equilibrium position in the medium to compression or rarefaction is the amplitude.

Period and Frequency

The time taken by the wave to move one wavelength is known as the period. The frequency of the longitudinal wave is the number of wavelengths per second.

Difference Between Longitudinal And Transverse Wave

Read More: Difference Between Longitudinal Waves and Transverse Waves

Frequently Asked Questions – FAQs

The longitudinal wave formula is given by the equation _____., list the characteristics of sound.

The characteristics of the sound are as follows:

What happens when a pebble is dropped into a pond with still water?

State true or false: mechanical waves are also known as elastic waves., name the condition in which sound waves can travel through the gas., what is a mechanical wave.

A mechanical wave is a type of wave that is generated by the oscillation matter, which transmits energy through the propagating medium.

What are the two types of mechanical waves?

Longitudinal waves and transverse waves are the two types of mechanical waves.

What is meant by a longitudinal wave?

A longitudinal wave is a type of wave in which the medium’s vibration is parallel to the direction of the wave, and the medium’s displacement is in the same direction as that of the wave movement.

What are the main characteristics of a longitudinal wave?

Compression, rarefaction, wavelength, amplitude, period and frequency are the main characteristics of a longitudinal wave.

What are the familiar examples of longitudinal waves?

Tsunami waves, seismic-P waves, sound waves, and vibration in spring are some of the familiar examples of longitudinal waves.

What are the main differences between a Longitudinal wave and a transverse wave?

A longitudinal wave is a type of wave that travels in the direction of the medium, but a transverse wave is another type of wave that travels in the direction of the medium. Longitudinal waves are made of compressions and rarefactions, while transverse waves are made of crests and troughs.

What is constructive interference?

What is a transverse wave, what are longitudinal waves, define amplitude., what is wavelength.

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Acoustics and Vibration Animations

Daniel A. Russell , Graduate Program in Acoustics, The Pennsylvania State University

All text and images on this page are ©1998-2013 by Daniel A. Russell and may not used in other web pages or reports without permission .

The content of this page was originally posted on August 26, 1998 . Animations were last updated on August 5, 2016 . The HTML code was modified to be HTML5 compliant on March 18, 2013.

Longitudinal and Transverse Wave Motion

Mechanical Waves are waves which propagate through a material medium (solid, liquid, or gas) at a wave speed which depends on the elastic and inertial properties of that medium. There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves. The animations below demonstrate both types of wave and illustrate the difference between the motion of the wave and the motion of the particles in the medium through which the wave is travelling.

The following animations were created using a modifed version of the Mathematica ® Notebook " Sound Waves " by Mats Bengtsson.

Longitudinal Waves

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation at right shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

The P waves (Primary waves) in an earthquake are examples of Longitudinal waves. The P waves travel with the fastest velocity and are the first to arrive.

Transverse Waves

The S waves (Secondary waves) in an earthquake are examples of Transverse waves. S waves propagate with a velocity slower than P waves, arriving several seconds later.

Water Waves (updated 2016)

Rayleigh surface waves (updated 2016).

The following animation was produced with a Mathematica notebook, Rayleigh-v8.nb , which I created to investigate the behavior of Rayleigh waves which occur in solids. This Mathematica notebook contains several other graphs which further analyzer the behavior of Rayleigh waves.

Another example of waves with both longitudinal and transverse motion may be found in solids as Rayleigh surface waves (named after John W. Strutt, 3rd Baron Rayleigh who first studied them in 1885). The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases.

Rayleigh waves in an elastic solid are different from surface waves in water in a very important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counter-clockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. This motion is often referred to as being "retrograde" since at the surface, the horizontal component of the particle motion is in the opposite direction as the wave propagation direction. I have identified two particles in orange in this animation to illustrate the retrograde elliptical path at the surface and the reversal in the direction of motion as a function of depth.

The Rayleigh surface waves are the waves that cause the most damage during an earthquake. They travel with velocities slower than S waves, and arrive later, but with much greater amplitudes. These are also the waves that are most easily felt during an earthquake and involve both up-down and side-to-side motion.

Update (Aug. 5, 2016) : Thanks to Dongyao Li (graduate student at the University of Illinois, Urbana-Champaign) who asked questions resulting in a much improved version of this animation.

Transverse and Longitudinal Waves

Andre Beroukhim

Short Description of Topic

Waves are the way in which energy is transferred. Of the many different types of waves, some can be divided into either transverse or longitudinal waves. Definitions:

For Longitudinal waves, the displacement of the medium is parallel to the direction of propagation of the wave (direction of the wave's travel)

For Transverse waves, the displacement of the medium is perpendicular to the direction of propagation of the wave (direction of the wave's travel)

• 1.1 A Mathematical Model
• 1.2 A Computational Model
• 2.2 Middling
• 2.3 Difficult
• 3 Connectedness
• 5.1 Further reading
• 5.2 External links
• 6 References

The Main Idea

State, in your own words, the main idea for this topic

The idea behind this topic is to compare two types of waves and the ways in which they can be found in real life. Nearly any type of wave can be defined as a transverse or a longitudinal wave and the ability to categorize waves into these two categories is extremely useful for energy transfer concepts. To elaborate -- consider light, which is a transverse wave. Light waves can pass through particles that have tigthly packed particles, and these particles in the wave collide with those in the medium, which is why light passes through different mediums with different refraction patterns. Longitudinal waves, such as sound for example, travel directly parallel to the energy transfer. A nice real life example to think of is how we can hear things from outside a room if just the door is opened -- because sound can bend from outside to the door into the room. Light however, does not bend as easily which is why we won't see a lot of light when in a room with just the door open. This example is just one of the many where transverse and longitudinal waves demonstrate different properties.

Comparing the two wave types: [1]

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

TRANSVERSE WAVES

Sin Curves are directly related to ocean waves because of their visual rate of flow as well as how they transfer energy! Think about surfing - it's much easier to surf if you understand how the water is moving and what patterns it produces.

LONGITUDINAL WAVES

How does momentum and impulse transfer through a slinky (Wave)? [3]

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Transverse [4]

Question 1: Compare a Transverse Wave to a Sin curve. What are 4 properties of trigonometric curves (think Asin(Bx+C)+D)? What is the top point called? Bottom point?

Q2: What sort of energy is mainly transferred in a wave on the sea: Heat, Kinetic, or Potential?

Q3: If you float in gentle waves - in what direction do you move ?

Question 1: [5]

Q2: In what direction do the water particles move in a wave: Toward you, away from you, or up and down?

Q4: If the amplitude of a sound wave is altered - what changes? Loudness, pitch, or frequency?

Q1 Longitudinal: [7]

Q2 Transverse:

Logan, Cassie and Abbey are doing the Pulse Speed Lab. Logan and Cassie stand 6.8 m apart and stretch a zinc-coiled snakey between them. Logan introduces a pulse into the snakey at his end. Using a stopwatch, Abbey measures that it takes 15.1 seconds for the pulse to travel to Cassie's end and back two times. They then repeat the experiment with a copper-coiled snakey stretched the same distance and find that pulses travel back and forth two times in 16.9 seconds. a. Determine the speed of the pulse in the zinc-coiled snakey. b. Determine the speed of the pulse in the copper-coiled snakey.

Connectedness

• How is this topic connected to something that you are interested in?

Sound and light are some of the most intriguing ideas to me, hugely in part due to the fact that there is so much detail revolving around how they work and what makes them unique waves. So after discovering that both are their own unique type of wave, transverse and longitudinal, I was really interested to see what properties they did and didn't share. Eventually I found out how broadly the topic of these both waves can expand to.

• How is it connected to your major?

IE is about solving problems efficiently and effectively. This may generally seem like a more ME-related topic, but I believe that there are tons of ways in which understanding how energy propagation works can lead to perfecting that propagation -- if a sound wave is emitted from a product that doesn't require sound, how can we get rid of it? How can we maximize the effectiveness of solar panels? How can we capture sound energy? It's even something that we refer to in physics class - many times in some unideal experiments or examples there is a loss of energy in the form of sound.

• Is there an interesting industrial application?

Similar to ideas I previously mentioned.

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

This section contains the the references you used while writing this page

For example Questions:

http://www.ewart.org.uk/science/waves/wav1.htm

http://www.physicsclassroom.com/calcpad/waves/problems

http://www.varsitytutors.com/mcat_physical-help/longitudinal-and-transverse-waves

Other: https://evantoh23.files.wordpress.com/2011/07/rope_waves.jpg http://ef.engr.utk.edu/hyperphysics/hbase/Sound/imgsou/pond2.gif

• Which Category did you place this in?

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Longitudinal Waves

Grade 6 science worksheets.

Longitudinal waves are a type of wave that travels through a medium in which the particles of the medium move parallel to the direction of wave propagation. This means that the wave energy is transferred in the same direction as the particle motion.

Table of Contents:

What are Longitudinal Waves?

• Formulae for Longitudinal Waves

Characteristics of Longitudinal Waves

Applications of longitudinal waves.

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One example of a longitudinal wave is sound waves, created by an object’s vibration and travel through the air or other media as a series of compressions and rarefactions.

In compression, the air particles are tightly packed together, while in a rarefaction, the air particles are spread out. The sound wave travels as a series of these compressions and rarefactions through the medium, transferring energy from the source of the sound to the receiver.

Another example of longitudinal waves is seismic waves, which travel through the Earth’s interior and are generated by earthquakes or other seismic events. There are two types of seismic waves: P-waves, which are longitudinal waves that travel through solids and liquids, and gas and S-waves, which are transverse waves that only travel through solids.

Longitudinal waves can be used in a variety of applications, including medical imaging, where ultrasound waves are used to create images of the internal structures of the body, and in non-destructive testing, which is a technique used to test the structural integrity of materials without damaging them.

The formula for the speed of longitudinal waves is given by:

v is the speed of the wave in meters per second (m/s)

B is the bulk modulus of the medium in pascals (Pa)

For different mediums, B represents different quantities.

For solid medium, B represents Young’s modulus.

For liquid medium, B represents the Shear modulus.

For gas medium, B represents Bulk modulus.

ρ is the density of the medium in kilograms per cubic meter (kg/m³)

The bulk modulus is a measure of the resistance of a material to compression, and the density is the mass per unit volume. This formula is based on the assumption that the longitudinal wave is traveling through a homogeneous medium with constant bulk modulus and density.

This formula can be used to calculate the speed of sound waves, which are longitudinal waves that travel through air, water, and other fluids. The speed of sound in air at room temperature and standard atmospheric pressure is approximately 343 meters per second. The speed of sound in other media, such as liquids and solids, depends on the density and elasticity of the medium.

Particle Motion: In longitudinal waves, the particles of the medium move parallel to the direction of wave propagation. This means the wave energy is transferred in the same direction as the particle motion.

Compression and Rarefaction: A longitudinal wave is a series of compressions and rarefactions. In compression, the particles of the medium are tightly packed together, while in a rarefaction, the particles are spread out.

Speed: The speed of a longitudinal wave is determined by the properties of the medium it travels through, such as its density and elasticity.

Wavelength: The wavelength of a longitudinal wave is the distance between two adjacent compressions or rarefactions.

Frequency: The frequency of a longitudinal wave is the number of complete cycles (peaks or troughs) that pass a given point in one second.

Amplitude: The amplitude of a longitudinal wave is the maximum displacement of the particles of the medium from their resting position. It is related to the energy carried by the wave.

Interference: Like all waves, longitudinal waves can undergo interference, where two or more waves meet and either reinforce or cancel each other out.

Reflection and Refraction: Longitudinal waves can also undergo reflection and refraction when they encounter boundaries or move from one medium to another with different properties.

Understanding the characteristics of longitudinal waves is important in many fields, including physics, engineering, and medicine.

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Here are some examples of longitudinal waves and their applications:

Sound Waves: Sound waves are longitudinal waves that travel through a medium, such as air, water, or solid materials. They are used in a wide range of applications, including communication, music, and medical imaging. For example, ultrasound waves are used in medical imaging to create images of the internal structures of the body.

Seismic Waves: Seismic waves are longitudinal waves that travel through the Earth’s interior and are generated by earthquakes or other seismic events. They are used to study the Earth’s interior and to detect and measure earthquakes.

Pressure Waves: Pressure waves are longitudinal waves that travel through fluids, such as gasses and liquids. They are used in a variety of applications, including in chemical processing, where pressure waves can be used to mix or separate fluids.

Ultrasound Waves: Ultrasound waves are high-frequency sound waves that are used in medical imaging, cleaning, and welding. They are also used in industrial testing to detect flaws in materials.

Shock Waves: Shock waves are high-intensity longitudinal waves that are produced by explosions or other high-energy events. They are used in a variety of applications, including in medical treatments for kidney stones and in industrial processes for cutting, welding, and forming materials.

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Longitudinal Waves FAQS

What is the difference between longitudinal and transverse waves.

Longitudinal waves are waves in which the particles of the medium vibrate parallel to the direction of wave propagation, while transverse waves are waves in which the particles vibrate perpendicular to the direction of wave propagation.

What is an example of a longitudinal wave?

Sound waves are an example of longitudinal waves. They travel through a medium, such as air, and are characterized by compressions and rarefactions.

What is the formula for the speed of longitudinal waves?

The speed of longitudinal waves is given by the formula v = √(B/ρ), where v is the speed of the wave, B is the bulk modulus of the medium, and ρ is the density of the medium.

How are longitudinal waves used in medical imaging?

Ultrasound waves are longitudinal waves that are used in medical imaging to create images of the internal structures of the body. By emitting and receiving high-frequency sound waves, doctors can create images of organs, tissues, and other structures.

What is the difference between longitudinal and surface waves?

Longitudinal waves travel through a medium, while surface waves travel along the boundary between two media. Surface waves are a combination of longitudinal and transverse waves.

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Longitudinal Waves

Longitudinal Waves are a type of mechanical wave in which the particle oscillates parallel to the direction of the wave. The displacement of the medium in a longitudinal wave is along the direction of wave propagation. Examples of longitudinal waves include sound waves, seismic P waves, ultrasound waves, etc.

In this article, we will learn about Longitudinal Waves, their definition, formula, and examples, along with a comparison with transverse waves.

Table of Content

What are Longitudinal Waves?

Examples of longitudinal waves, longitudinal waves formula, longitudinal waves formulas, formation of longitudinal waves, longitudinal wave of sound, longitudinal waves of pressure, parts of longitudinal wave, longitudinal wave diagram, longitudinal waves characteristics, particle vibration, difference between longitudinal waves and transverse waves.

Longitudinal Waves are a type of mechanical wave in which the waves travel adjacent to the direction of the wave propagation. In this wave, each particle of matter vibrates in its normal position along the axis of propagation, causing alternative regions of compression and rarefaction in the medium. The distance between two compression or two rarefactions is known as wavelength.

When the region of compression and rarefaction coincide with each other, it is called constructive interference, and when they do not coincide, it is known as destructive interference . As these waves produce compression and rarefaction, they are also known as compression waves. The oscillation in longitudinal waves is such that the wave moves in a direction parallel to the direction of the vibration of the medium.

Longitudinal Waves Definition

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction of the wave travels, and the displacement of the medium is in the same direction as the wave propagation.

Here are some examples of longitudinal waves in detail:

• Sound Waves: Sound waves are a common example of longitudinal waves. When a sound is produced, the particles in the surrounding medium (such as air) oscillate back and forth, creating a longitudinal wave.
• Seismic P-waves: Seismic P-waves are longitudinal waves that travel through the Earth’s crust. These waves are generated by the sudden release of energy, such as during an earthquake. The vibrations of the Earth’s crust create alternating regions of compression and rarefaction, which propagate as longitudinal waves.
• Ultrasound Waves: Ultrasound waves are longitudinal waves created by a transducer’s vibration and propagate through a medium, such as human tissue or a solid object. The particles in the medium oscillate back and forth, creating a longitudinal wave.
• Vibration of a Spring: When a coiled spring is compressed at one end and released, it experiences a wave of compression followed by a stretching. This vibration is an example of a longitudinal wave, as the particles in the spring oscillate back and forth about their equilibrium position.

The following formula can describe longitudinal waves:

y(x, t)= A cos(2πx/λ – 2πft + ϕ) Where: y is the displacement of the point on the travelling wave x is the distance from the point to the wave’s source t is the time elapsed A is the amplitude of the oscillations λ is the wavelength f is the frequency ϕ is the phase angle

In the case of longitudinal harmonic sound waves, the formula can be written as:

y(x, t) = y 0 cos (ω(t-x/c)) Where: y 0 is the amplitude of the oscillations ω is the angular frequency of the wave c is the speed of the wave

A table containing all the formulas related to the longitudinal wave is given below:

Longitudinal waves are formed when a disturbance or vibration occurs in a medium, causing the medium particles to oscillate back and forth in the same direction as the wave’s propagation.

This disturbance can be caused by a variety of sources, such as a vibrating object or a sudden pressure change. As the particles of the medium oscillate, they create regions of compression and rarefaction, which propagate through the medium as a longitudinal wave.

Check: Electromagnetic Waves

Sound waves are longitudinal waves, which means that the vibrations of the particles in the medium are parallel to the direction the wave travels. In other words, the particles of the medium vibrate back and forth in the same direction as the wave movement. As the sound wave travels through the medium, it creates compressions and rarefactions, which are areas of high and low pressure, respectively.

When an electrical signal is sent to a speaker, it causes a coil of wire within the speaker to vibrate rapidly. This vibration, in turn, moves a cone-shaped diaphragm back and forth, pushing and pulling on the surrounding air particles. This creates sound waves that travel through the air, allowing us to hear the sound produced by the speaker.

Propagation of Sound Wave Frequency and Wavelength of Sound Wave

Longitudinal waves of pressure, also known as pressure waves, describe a type of mechanical wave where particles within the medium oscillate in the same direction as the wave’s propagation.

A harmonic pressure wave oscillation will be, y(x,t)=y0cos(kx-ωt+φ)

y0 is the amplitude of displacement

k is the wavenumber

x is the distance along the axis of propagation

ω is the angular frequency

t is the time

φ is the phase difference

The following properties characterize longitudinal waves:

Compression: Longitudinal waves have regions of high pressure called compressions, where particles are close to each other.

Rarefaction: Rarefactions are the regions of low pressure, where particles are spread further apart. Note: In longitudinal waves, the particles in areas of compression are closer together than on average, while in areas of rarefaction, the particles are further apart than on average.

Wavelength: The wavelength of a longitudinal wave is the distance between two consecutive compressions or rarefactions.

Amplitude: It is the maximum displacement of a point on the wave from its rest position.

Period: The period is the time taken by the wave to complete one wavelength.

Frequency: Frequency of longitudinal wave is the number of wavelengths per second.

Longitudinal Wave Diagram explaining compression, rarefaction and wavelength is given below:

longitudinal wave

Check: Refraction of Sound – Definition, Echo, Examples, and FAQs

The characteristics of longitudinal waves are:

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels, and the displacement of the medium is in the same direction as the wave’s propagation. These waves can be observed in various media, such as solids, liquids, and gases.

The velocity of longitudinal waves depends on the properties of the medium, such as its density and elastic properties, rather than the source of the wave. For example, the speed of sound in a medium is primarily determined by the medium’s properties, not the intensity of the sound produced.

In the context of longitudinal waves, the forward velocity of a longitudinal wave is given by the formula:

v= λ/T = ω/k Where: v is the velocity of the wave λ is the wavelength of the wave T is the period of the wave ω is the angular frequency of the wave k is the wave vector

Some key points about the velocity of longitudinal waves include:

• The velocity of longitudinal waves is directly proportional to the wavelength and inversely proportional to the period.
• The velocity of longitudinal waves is also directly proportional to the angular frequency and inversely proportional to the wave vector.
• The velocity of longitudinal waves is independent of the amplitude of the wave.

In longitudinal waves, the particles of the medium vibrate parallel to the direction the wave travels, and their displacement is in the same direction as the wave’s propagation. Some critical aspects of particle vibration in longitudinal waves include:

• As the wave travels, the particles create regions of compression (where the particles are squashed together) and rarefaction (where the particles move apart). These regions alternate along the wave’s path.
• The particles of the medium do not move with the wave; they simply oscillate back and forth about their individual equilibrium positions.
• When the wave passes, the particles return to their equilibrium position.

Check: Introduction to Waves – Definition, Types, Properties

The basic difference between Longitudinal and Transverse wave is given below:

Wave Types of Wave Difference between longitudinal and transverse wave

Longitudinal Waves: FAQs

What is longitudinal waves.

Longitudinal waves are a type of mechanical wave where the particles in the medium move parallel to the direction of wave propagation. Each particle vibrates along the axis of propagation, causing regions of compression and rarefaction.

What are Transversal Waves?

Transverse waves are another type of mechanical wave where particles move perpendicular to the direction of wave propagation. They exhibit crests and troughs in their oscillation.

What is Amplitude of Longitudinal Wave?

Amplitude of Longitudinal wave is the maximum displacement of a point on the wave from its rest position.

Sound Wave is Longitudinal Wave or Transverse Wave?

Sound wave is longitudinal wave because their oscillations are parallel to the direction of wave propagation.

What are Three Examples of Longitudinal Waves?

Sound Waves, Seismic P-waves, and Ultrasound Waves are three examples of Longitudinal Waves.

What is another Name of Longitudinal waves?

Longitudinal waves are also known as compression waves due to the alternate regions of compression and rarefaction they create in the medium.

Distinguish Between Transverse and Longitudinal Waves?

Transverse waves exhibit vibrations perpendicular to the direction of wave propagation, while longitudinal waves show vibrations parallel to the wave’s direction.

What are Compression and Rarefaction in Longitudinal Waves?

Compression and rarefaction represent areas of high and low particle density, respectively, contributing to the wave’s energy transfer and propagation.

Is Light Longitudinal or Transverse?

Light is a transverse wave. Unlike longitudinal waves, light’s vibrations occur perpendicular to its direction of propagation, involving electric and magnetic fields oriented at right angles to the wave’s path.

Is Water Wave Longitudinal or Transverse?

Water waves are mainly transverse, with particles moving up and down perpendicular to the wave direction. Some longitudinal aspects may exist, particularly in deeper layers.

What is Speed of Longitudinal Wave?

The speed of a longitudinal wave depends on the medium’s properties. The velocity is determined by factors like density and elastic properties, following the formula v = λ/T = ω/k , where v is velocity, λ is wavelength, T is period, ω is angular frequency, and k is wave vector.

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Transverse and Longitudinal Waves: Review and Examples

• The Albert Team
• Last Updated On: August 30, 2023

Waves are everywhere – from the strings of musical instruments to the sounds we hear daily. In this post, we’ll break down two main types of waves: transverse and longitudinal waves. We’ll explain how they differ, what they have in common, and content like crests, troughs, and other parts of a wave. By the end, you’ll have a clear grasp of these physics concepts.

Mechanical Waves

Waves are more than just oscillations; they carry energy from one place to another, affecting our world in countless ways. In the realm of physics, mechanical waves are the archetype of such phenomena.

Defining Mechanical Waves

Mechanical waves are disturbances that travel through a medium, transferring energy as they go. This energy transfer is due to particles in the medium moving or oscillating. For a mechanical wave to exist, it’s crucial to have a medium; this can be solid, liquid, or gas. In essence, when energy is introduced, say by plucking a guitar string, it causes a disturbance which then travels via the medium – in this case, the string and the surrounding air.

Transverse and Longitudinal Waves

Mechanical waves can be broadly categorized into two types:

• Transverse Waves: In these waves, the particle displacement is perpendicular to the direction of the wave propagation. Think of a wavy flag or the surface of water when a stone is tossed in; you’re witnessing transverse waves. A notable feature here is the crest (the highest point of the wave) and the trough (the lowest point).
• Longitudinal Waves: For these waves, particles of the medium move in a direction parallel to the wave’s direction of travel. Sound waves are a classic example. In these waves, compressions (areas where particles are close together) and rarefactions (areas where particles are spread apart) are observed.

Understanding mechanical waves and their types helps us learn more about waves in general. With this basic knowledge, we can further study their properties and see how they affect our everyday lives.

What is a Transverse Wave?

Transverse waves are a type of mechanical wave where the motion of the medium’s particles is perpendicular to the direction of the wave’s propagation. Imagine you’re holding one end of a rope and you give it a sharp flick upwards. The bump or wave travels horizontally, while the rope moves up and down—this motion is what defines a transverse wave.

Visual Representation of a Transverse Wave

Picture a flat, calm sea. When a pebble is dropped into the water, ripples spread outward in concentric circles. If you were to look closely at any point on a ripple, you’d notice that the water moves up and down while the ripple moves outward. The up-and-down movement of the water particles is perpendicular to the ripple’s outward motion.

View the video to see a transverse wave along a slinky coil.

Crests and Troughs

Two primary features of a transverse wave are its crests and troughs.

• Crests: The crest is the highest point, where the medium (like the water or rope) rises to its maximum height.
• Troughs: The trough is the lowest point, where it dips down. The distance from a crest to the next crest or from one trough to the next defines the wave’s wavelength.

Examples of Transverse Waves

One of the most common examples of a transverse wave is light. While we can’t see the actual oscillations of light waves, they move in a transverse manner. Another tangible example is a guitar string. When plucked, the string moves up and down, creating a transverse wave, which then produces a sound. This up-and-down motion is perpendicular to the direction in which the wave travels along the string.

What is a Longitudinal Wave?

Longitudinal waves involve oscillations that occur in the same direction as the wave’s propagation. In simple terms, the particles of the medium move back and forth along the direction the wave is traveling, rather than moving up and down like in transverse waves.

Visual Representation of a Longitudinal Wave

Imagine a slinky toy. If you compress a few coils at one end and then release them, you’ll see a bunching and spreading effect traveling down the length of the slinky. This bunching and spreading motion, occurring in the same direction the disturbance is moving, represents a longitudinal wave.

The following video shows a longitudinal wave along a slinky coil.

Compressions and Rarefactions

Central to understanding longitudinal waves are the concepts of compressions and rarefactions.

• Compressions: These are regions where particles of the medium are closer together, or more bunched up. Using the slinky example, compressions are the areas where the coils are close to each other.
• Rarefactions: These are areas where particles are spread out or less dense. In the context of the slinky, rarefactions are the stretches where the coils are spaced farther apart.

These features in longitudinal waves are analogous to the crests and troughs seen in transverse waves.

Example of Longitudinal Waves

The most relatable example of a longitudinal wave is sound. When something makes a noise, it sends out vibrations (or pressure changes) in the surrounding air. As these vibrations travel, they cause air molecules to bunch up in compressions and spread out in rarefactions. It’s this back-and-forth motion of molecules, in the direction the sound is traveling, that lets us hear sounds, whether it’s a song on the radio or the chime of a bell.

Common Misconception

When navigating the world of waves, it’s easy to misunderstand or conflate certain ideas. As we further our exploration of transverse and longitudinal waves, it’s important to address and clarify some of the most common misconceptions.

The Difference Between Transverse and Longitudinal Waves

A significant point of confusion lies in distinguishing between the two types of waves. Many assume that transverse waves only occur on the surface of mediums, like the surface of water, while longitudinal waves are restricted to the interior of materials. Transverse waves can also propagate within a medium, just like light through a glass prism. Similarly, while sound (a longitudinal wave) often travels within a medium like air, there can be surface longitudinal waves in certain contexts, like in seismology.

Additionally, some believe that transverse waves are only related to electromagnetic phenomena, like light. While light is indeed a transverse wave, not all transverse waves are electromagnetic in nature. The ripples on a pond or vibrations on a string are mechanical transverse waves.

What Do Longitudinal and Transverse Waves Have in Common?

With the evident differences, people often overlook the shared characteristics of these wave types. One misconception is that transverse and longitudinal waves are entirely distinct with no shared properties. However, both types of waves can transport energy without the net movement of the medium they’re traveling in. For instance, while a sound wave (longitudinal) can transfer sound energy across a room, the air molecules in the room mostly return to their original positions. Similarly, while a plucked guitar string (transverse wave) vibrates visibly, the string doesn’t move away from the guitar.

We use waves every day, from listening to music to talking with friends. This post broke down the basics of transverse and longitudinal waves, showing how they work, what they look like, and where we might encounter them. We also tackled some common misunderstandings about these waves. By now, you should have a clearer idea of these key physics topics and how they touch our daily lives.

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Sound as a Longitudinal Wave

• Sound is a Mechanical Wave
• Sound is a Longitudinal Wave
• Sound is a Pressure Wave

Sound waves in air (and any fluid medium) are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves. A vibrating string can create longitudinal waves as depicted in the animation below. As the vibrating string moves in the forward direction, it begins to push upon surrounding air molecules, moving them to the right towards their nearest neighbor. This causes the air molecules to the right of the string to be compressed into a small region of space. As the vibrating string moves in the reverse direction (leftward), it lowers the pressure of the air immediately to its right, thus causing air molecules to move back leftward. The lower pressure to the right of the string causes air molecules in that region immediately to the right of the string to expand into a large region of space. The back and forth vibration of the string causes individual air molecules (or a layer of air molecules) in the region immediately to the right of the string to continually vibrate back and forth horizontally. The molecules move rightward as the string moves rightward and then leftward as the string moves leftward. These back and forth vibrations are imparted to adjacent neighbors by particle-to-particle interaction. Other surrounding particles begin to move rightward and leftward, thus sending a wave to the right. Since air molecules (the particles of the medium) are moving in a direction that is parallel to the direction that the wave moves, the sound wave is referred to as a longitudinal wave. The result of such longitudinal vibrations is the creation of compressions and rarefactions within the air.

Regardless of the source of the sound wave - whether it is a vibrating string or the vibrating tines of a tuning fork - sound waves traveling through air are longitudinal waves. And the essential characteristic of a longitudinal wave that distinguishes it from other types of waves is that the particles of the medium move in a direction parallel to the direction of energy transport.

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Learning objectives.

By the end of this section, you will be able to:

• Describe the basic characteristics of wave motion
• Define the terms wavelength, amplitude, period, frequency, and wave speed
• Explain the difference between longitudinal and transverse waves, and give examples of each type
• List the different types of waves

We saw in Oscillations that oscillatory motion is an important type of behavior that can be used to model a wide range of physical phenomena. Oscillatory motion is also important because oscillations can generate waves, which are of fundamental importance in physics. Many of the terms and equations we studied in the chapter on oscillations apply equally well to wave motion ( (Figure) ).

Figure 16.2 From the world of renewable energy sources comes the electric power-generating buoy. Although there are many versions, this one converts the up-and-down motion, as well as side-to-side motion, of the buoy into rotational motion in order to turn an electric generator, which stores the energy in batteries.

Types of Waves

A wave is a disturbance that propagates, or moves from the place it was created. There are three basic types of waves: mechanical waves, electromagnetic waves, and matter waves.

Basic mechanical waves are governed by Newton’s laws and require a medium. A medium is the substance a mechanical waves propagates through, and the medium produces an elastic restoring force when it is deformed. Mechanical waves transfer energy and momentum, without transferring mass. Some examples of mechanical waves are water waves, sound waves, and seismic waves. The medium for water waves is water; for sound waves, the medium is usually air. (Sound waves can travel in other media as well; we will look at that in more detail in Sound .) For surface water waves, the disturbance occurs on the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly. For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker or a vibrating tuning fork. In both cases, the disturbance is the oscillation of the molecules of the fluid. In mechanical waves, energy and momentum transfer with the motion of the wave, whereas the mass oscillates around an equilibrium point. (We discuss this in Energy and Power of a Wave .) Earthquakes generate seismic waves from several types of disturbances, including the disturbance of Earth’s surface and pressure disturbances under the surface. Seismic waves travel through the solids and liquids that form Earth. In this chapter, we focus on mechanical waves.

Electromagnetic waves are associated with oscillations in electric and magnetic fields and do not require a medium. Examples include gamma rays, X-rays, ultraviolet waves, visible light, infrared waves, microwaves, and radio waves. Electromagnetic waves can travel through a vacuum at the speed of light, [latex] v=c=2.99792458\,×\,{10}^{8}\,\text{m/s}. [/latex] For example, light from distant stars travels through the vacuum of space and reaches Earth. Electromagnetic waves have some characteristics that are similar to mechanical waves; they are covered in more detail in Electromagnetic Waves in volume 2 of this text.

Matter waves are a central part of the branch of physics known as quantum mechanics. These waves are associated with protons, electrons, neutrons, and other fundamental particles found in nature. The theory that all types of matter have wave-like properties was first proposed by Louis de Broglie in 1924. Matter waves are discussed in Photons and Matter Waves in the third volume of this text.

Mechanical Waves

Mechanical waves exhibit characteristics common to all waves, such as amplitude, wavelength, period, frequency, and energy. All wave characteristics can be described by a small set of underlying principles.

The simplest mechanical waves repeat themselves for several cycles and are associated with simple harmonic motion. These simple harmonic waves can be modeled using some combination of sine and cosine functions. For example, consider the simplified surface water wave that moves across the surface of water as illustrated in (Figure) . Unlike complex ocean waves, in surface water waves, the medium, in this case water, moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. In (Figure) , the waves causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The crest is the highest point of the wave, and the trough is the lowest part of the wave. The time for one complete oscillation of the up-and-down motion is the wave’s period T . The wave’s frequency is the number of waves that pass through a point per unit time and is equal to [latex] f=1\text{/}T. [/latex] The period can be expressed using any convenient unit of time but is usually measured in seconds; frequency is usually measured in hertz (Hz), where [latex] 1\,{\text{Hz}=1\,\text{s}}^{-1}. [/latex]

The length of the wave is called the wavelength and is represented by the Greek letter lambda [latex] (\lambda ) [/latex], which is measured in any convenient unit of length, such as a centimeter or meter. The wavelength can be measured between any two similar points along the medium that have the same height and the same slope. In (Figure) , the wavelength is shown measured between two crests. As stated above, the period of the wave is equal to the time for one oscillation, but it is also equal to the time for one wavelength to pass through a point along the wave’s path.

The amplitude of the wave ( A ) is a measure of the maximum displacement of the medium from its equilibrium position. In the figure, the equilibrium position is indicated by the dotted line, which is the height of the water if there were no waves moving through it. In this case, the wave is symmetrical, the crest of the wave is a distance [latex] \text{+}A [/latex] above the equilibrium position, and the trough is a distance [latex] \text{−}A [/latex] below the equilibrium position. The units for the amplitude can be centimeters or meters, or any convenient unit of distance.

Figure 16.3 An idealized surface water wave passes under a seagull that bobs up and down in simple harmonic motion. The wave has a wavelength [latex] \lambda [/latex], which is the distance between adjacent identical parts of the wave. The amplitude A of the wave is the maximum displacement of the wave from the equilibrium position, which is indicated by the dotted line. In this example, the medium moves up and down, whereas the disturbance of the surface propagates parallel to the surface at a speed v.

The water wave in the figure moves through the medium with a propagation velocity [latex] \overset{\to }{v}. [/latex] The magnitude of the wave velocity is the distance the wave travels in a given time, which is one wavelength in the time of one period, and the wave speed is the magnitude of wave velocity. In equation form, this is

This fundamental relationship holds for all types of waves. For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light.

Transverse and Longitudinal Waves

We have seen that a simple mechanical wave consists of a periodic disturbance that propagates from one place to another through a medium. In (Figure) (a), the wave propagates in the horizontal direction, whereas the medium is disturbed in the vertical direction. Such a wave is called a transverse wave . In a transverse wave, the wave may propagate in any direction, but the disturbance of the medium is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. (Figure) (b) shows an example of a longitudinal wave. The size of the disturbance is its amplitude A and is completely independent of the speed of propagation v .

Figure 16.4 (a) In a transverse wave, the medium oscillates perpendicular to the wave velocity. Here, the spring moves vertically up and down, while the wave propagates horizontally to the right. (b) In a longitudinal wave, the medium oscillates parallel to the propagation of the wave. In this case, the spring oscillates back and forth, while the wave propagates to the right.

A simple graphical representation of a section of the spring shown in (Figure) (b) is shown in (Figure) . (Figure) (a) shows the equilibrium position of the spring before any waves move down it. A point on the spring is marked with a blue dot. (Figure) (b) through (g) show snapshots of the spring taken one-quarter of a period apart, sometime after the end of` the spring is oscillated back and forth in the x -direction at a constant frequency. The disturbance of the wave is seen as the compressions and the expansions of the spring. Note that the blue dot oscillates around its equilibrium position a distance A , as the longitudinal wave moves in the positive x -direction with a constant speed. The distance A is the amplitude of the wave. The y -position of the dot does not change as the wave moves through the spring. The wavelength of the wave is measured in part (d). The wavelength depends on the speed of the wave and the frequency of the driving force.

Figure 16.5 (a) This is a simple, graphical representation of a section of the stretched spring shown in (Figure)(b), representing the spring’s equilibrium position before any waves are induced on the spring. A point on the spring is marked by a blue dot. (b–g) Longitudinal waves are created by oscillating the end of the spring (not shown) back and forth along the x-axis. The longitudinal wave, with a wavelength [latex] \lambda [/latex], moves along the spring in the +x-direction with a wave speed v. For convenience, the wavelength is measured in (d). Note that the point on the spring that was marked with the blue dot moves back and forth a distance A from the equilibrium position, oscillating around the equilibrium position of the point.

Waves may be transverse, longitudinal, or a combination of the two. Examples of transverse waves are the waves on stringed instruments or surface waves on water, such as ripples moving on a pond. Sound waves in air and water are longitudinal. With sound waves, the disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and for this reason, the sound waves in them are longitudinal waves. Sound in solids can have both longitudinal and transverse components, such as those in a seismic wave. Earthquakes generate seismic waves under Earth’s surface with both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). The components of seismic waves have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water. Ocean waves also have both transverse and longitudinal components.

Wave on a String

A student takes a 30.00-m-long string and attaches one end to the wall in the physics lab. The student then holds the free end of the rope, keeping the tension constant in the rope. The student then begins to send waves down the string by moving the end of the string up and down with a frequency of 2.00 Hz. The maximum displacement of the end of the string is 20.00 cm. The first wave hits the lab wall 6.00 s after it was created. (a) What is the speed of the wave? (b) What is the period of the wave? (c) What is the wavelength of the wave?

• The speed of the wave can be derived by dividing the distance traveled by the time.
• The period of the wave is the inverse of the frequency of the driving force.
• The wavelength can be found from the speed and the period [latex] v=\lambda \text{/}T. [/latex]
• The first wave traveled 30.00 m in 6.00 s: [latex] v=\frac{30.00\,\text{m}}{6.00\,\text{s}}=5.00\frac{\text{m}}{\text{s}}. [/latex]
• The period is equal to the inverse of the frequency: [latex] T=\frac{1}{f}=\frac{1}{2.00\,{\text{s}}^{-1}}=0.50\,\text{s}. [/latex]
• The wavelength is equal to the velocity times the period: [latex] \lambda =vT=5.00\frac{\text{m}}{\text{s}}(0.50\,\text{s})=2.50\,\text{m}. [/latex]

Significance

The frequency of the wave produced by an oscillating driving force is equal to the frequency of the driving force.

Check Your Understanding

When a guitar string is plucked, the guitar string oscillates as a result of waves moving through the string. The vibrations of the string cause the air molecules to oscillate, forming sound waves. The frequency of the sound waves is equal to the frequency of the vibrating string. Is the wavelength of the sound wave always equal to the wavelength of the waves on the string?

The wavelength of the waves depends on the frequency and the velocity of the wave. The frequency of the sound wave is equal to the frequency of the wave on the string. The wavelengths of the sound waves and the waves on the string are equal only if the velocities of the waves are the same, which is not always the case. If the speed of the sound wave is different from the speed of the wave on the string, the wavelengths are different. This velocity of sound waves will be discussed in Sound .

Characteristics of a Wave

A transverse mechanical wave propagates in the positive x -direction through a spring (as shown in (Figure) (a)) with a constant wave speed, and the medium oscillates between [latex] \text{+}A [/latex] and [latex] \text{−}A [/latex] around an equilibrium position. The graph in (Figure) shows the height of the spring ( y ) versus the position ( x ), where the x -axis points in the direction of propagation. The figure shows the height of the spring versus the x -position at [latex] t=0.00\,\text{s} [/latex] as a dotted line and the wave at [latex] t=3.00\,\text{s} [/latex] as a solid line. (a) Determine the wavelength and amplitude of the wave. (b) Find the propagation velocity of the wave. (c) Calculate the period and frequency of the wave.

Figure 16.6 A transverse wave shown at two instants of time.

• The amplitude and wavelength can be determined from the graph.
• Since the velocity is constant, the velocity of the wave can be found by dividing the distance traveled by the wave by the time it took the wave to travel the distance.
• The period can be found from [latex] v=\frac{\lambda }{T} [/latex] and the frequency from [latex] f=\frac{1}{T}. [/latex]

Figure 16.7 Characteristics of the wave marked on a graph of its displacement.

• The distance the wave traveled from time [latex] t=0.00\,\text{s} [/latex] to time [latex] t=3.00\,\text{s} [/latex] can be seen in the graph. Consider the red arrow, which shows the distance the crest has moved in 3 s. The distance is [latex] 8.00\,\text{cm}-2.00\,\text{cm}=6.00\,\text{cm}. [/latex] The velocity is [latex] v=\frac{\text{Δ}x}{\text{Δ}t}=\frac{8.00\,\text{cm}-2.00\,\text{cm}}{3.00\,\text{s}-0.00\,\text{s}}=2.00\,\text{cm/s}. [/latex]
• The period is [latex] T=\frac{\lambda }{v}=\frac{8.00\,\text{cm}}{2.00\,\text{cm/s}}=4.00\,\text{s} [/latex] and the frequency is [latex] f=\frac{1}{T}=\frac{1}{4.00\,\text{s}}=0.25\,\text{Hz}. [/latex]

Note that the wavelength can be found using any two successive identical points that repeat, having the same height and slope. You should choose two points that are most convenient. The displacement can also be found using any convenient point.

The propagation velocity of a transverse or longitudinal mechanical wave may be constant as the wave disturbance moves through the medium. Consider a transverse mechanical wave: Is the velocity of the medium also constant?

• A wave is a disturbance that moves from the point of origin with a wave velocity v .
• A wave has a wavelength [latex] \lambda [/latex], which is the distance between adjacent identical parts of the wave. Wave velocity and wavelength are related to the wave’s frequency and period by [latex] v=\frac{\lambda }{T}=\lambda f. [/latex]
• Mechanical waves are disturbances that move through a medium and are governed by Newton’s laws.
• Electromagnetic waves are disturbances in the electric and magnetic fields, and do not require a medium.
• Matter waves are a central part of quantum mechanics and are associated with protons, electrons, neutrons, and other fundamental particles found in nature.
• A transverse wave has a disturbance perpendicular to the wave’s direction of propagation, whereas a longitudinal wave has a disturbance parallel to its direction of propagation.

Conceptual Questions

Give one example of a transverse wave and one example of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.

A sinusoidal transverse wave has a wavelength of 2.80 m. It takes 0.10 s for a portion of the string at a position x to move from a maximum position of [latex] y=0.03\,\text{m} [/latex] to the equilibrium position [latex] y=0. [/latex] What are the period, frequency, and wave speed of the wave?

What is the difference between propagation speed and the frequency of a mechanical wave? Does one or both affect wavelength? If so, how?

Propagation speed is the speed of the wave propagating through the medium. If the wave speed is constant, the speed can be found by [latex] v=\frac{\lambda }{T}=\lambda f. [/latex] The frequency is the number of wave that pass a point per unit time. The wavelength is directly proportional to the wave speed and inversely proportional to the frequency.

Consider a stretched spring, such as a slinky. The stretched spring can support longitudinal waves and transverse waves. How can you produce transverse waves on the spring? How can you produce longitudinal waves on the spring?

Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?

No, the distance you move your hand up and down will determine the amplitude of the wave. The wavelength will depend on the frequency you move your hand up and down, and the speed of the wave through the spring.

A sinusoidal, transverse wave is produced on a stretched spring, having a period T . Each section of the spring moves perpendicular to the direction of propagation of the wave, in simple harmonic motion with an amplitude A . Does each section oscillate with the same period as the wave or a different period? If the amplitude of the transverse wave were doubled but the period stays the same, would your answer be the same?

An electromagnetic wave, such as light, does not require a medium. Can you think of an example that would support this claim?

Storms in the South Pacific can create waves that travel all the way to the California coast, 12,000 km away. How long does it take them to travel this distance if they travel at 15.0 m/s?

Waves on a swimming pool propagate at 0.75 m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.00 s. How far away is the other end of the pool?

[latex] 2d=vt⇒d=11.25\,\text{m} [/latex]

Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency?

How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00 m/s?

Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 8.00 m apart. If they shake the bridge twice per second, what is the propagation speed of the waves?

What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at a wave speed of 0.800 m/s?

[latex] v=f\lambda ⇒\lambda =0.400\,\text{m} [/latex]

What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?

Radio waves transmitted through empty space at the speed of light [latex] (v=c=3.00\,×\,{10}^{8}\,\text{m/s}) [/latex] by the Voyager spacecraft have a wavelength of 0.120 m. What is their frequency?

Your ear is capable of differentiating sounds that arrive at each ear just 0.34 ms apart, which is useful in determining where low frequency sound is originating from. (a) Suppose a low-frequency sound source is placed to the right of a person, whose ears are approximately 18 cm apart, and the speed of sound generated is 340 m/s. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear? (b) Assume the same person was scuba diving and a low-frequency sound source was to the right of the scuba diver. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear, if the speed of sound in water is 1500 m/s? (c) What is significant about the time interval of the two situations?

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)

a. The P-waves outrun the S-waves by a speed of [latex] v=3.20\,\text{km/s;} [/latex] therefore, [latex] \text{Δ}d=0.320\,\text{km}. [/latex] b. Since the uncertainty in the distance is less than a kilometer, our answer to part (a) does not seem to limit the detection of nuclear bomb detonations. However, if the velocities are uncertain, then the uncertainty in the distance would increase and could then make it difficult to identify the source of the seismic waves.

A Girl Scout is taking a 10.00-km hike to earn a merit badge. While on the hike, she sees a cliff some distance away. She wishes to estimate the time required to walk to the cliff. She knows that the speed of sound is approximately 343 meters per second. She yells and finds that the echo returns after approximately 2.00 seconds. If she can hike 1.00 km in 10 minutes, how long would it take her to reach the cliff?

A quality assurance engineer at a frying pan company is asked to qualify a new line of nonstick-coated frying pans. The coating needs to be 1.00 mm thick. One method to test the thickness is for the engineer to pick a percentage of the pans manufactured, strip off the coating, and measure the thickness using a micrometer. This method is a destructive testing method. Instead, the engineer decides that every frying pan will be tested using a nondestructive method. An ultrasonic transducer is used that produces sound waves with a frequency of [latex] f=25\,\text{kHz}. [/latex] The sound waves are sent through the coating and are reflected by the interface between the coating and the metal pan, and the time is recorded. The wavelength of the ultrasonic waves in the coating is 0.076 m. What should be the time recorded if the coating is the correct thickness (1.00 mm)?

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13.1 Types of Waves

Section learning objectives.

By the end of this section, you will be able to do the following:

• Define mechanical waves and medium, and relate the two
• Distinguish a pulse wave from a periodic wave
• Distinguish a longitudinal wave from a transverse wave and give examples of such waves

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (A) examine and describe oscillatory motion and wave propagation in various types of media.

Section Key Terms

Mechanical waves.

What do we mean when we say something is a wave? A wave is a disturbance that travels or propagates from the place where it was created. Waves transfer energy from one place to another, but they do not necessarily transfer any mass. Light, sound, and waves in the ocean are common examples of waves. Sound and water waves are mechanical waves ; meaning, they require a medium to travel through. The medium may be a solid, a liquid, or a gas, and the speed of the wave depends on the material properties of the medium through which it is traveling. However, light is not a mechanical wave; it can travel through a vacuum such as the empty parts of outer space.

A familiar wave that you can easily imagine is the water wave. For water waves, the disturbance is in the surface of the water, an example of which is the disturbance created by a rock thrown into a pond or by a swimmer splashing the water surface repeatedly. For sound waves, the disturbance is caused by a change in air pressure, an example of which is when the oscillating cone inside a speaker creates a disturbance. For earthquakes, there are several types of disturbances, which include the disturbance of Earth’s surface itself and the pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Because water waves are common and visible, visualizing water waves may help you in studying other types of waves, especially those that are not visible.

Water waves have characteristics common to all waves, such as amplitude , period , frequency , and energy , which we will discuss in the next section.

Misconception Alert

Many people think that water waves push water from one direction to another. In reality, however, the particles of water tend to stay in one location only, except for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water particles stay in one place. If you feel yourself being pushed in an ocean, what you feel is the energy of the wave, not the rush of water. If you put a cork in water that has waves, you will see that the water mostly moves it up and down.

[BL] [OL] [AL] Ask students to give examples of mechanical and nonmechanical waves.

Pulse Waves and Periodic Waves

If you drop a pebble into the water, only a few waves may be generated before the disturbance dies down, whereas in a wave pool, the waves are continuous. A pulse wave is a sudden disturbance in which only one wave or a few waves are generated, such as in the example of the pebble. Thunder and explosions also create pulse waves. A periodic wave repeats the same oscillation for several cycles, such as in the case of the wave pool, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth periodically through the same positions.

[BL] Any kind of wave, whether mechanical or nonmechanical, or transverse or longitudinal, can be in the form of a pulse wave or a periodic wave.

Consider the simplified water wave in Figure 13.2 . This wave is an up-and-down disturbance of the water surface, characterized by a sine wave pattern. The uppermost position is called the crest and the lowest is the trough . It causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs pass under the bird.

Longitudinal Waves and Transverse Waves

Mechanical waves are categorized by their type of motion and fall into any of two categories: transverse or longitudinal. Note that both transverse and longitudinal waves can be periodic. A transverse wave propagates so that the disturbance is perpendicular to the direction of propagation. An example of a transverse wave is shown in Figure 13.3 , where a woman moves a toy spring up and down, generating waves that propagate away from herself in the horizontal direction while disturbing the toy spring in the vertical direction.

In contrast, in a longitudinal wave , the disturbance is parallel to the direction of propagation. Figure 13.4 shows an example of a longitudinal wave, where the woman now creates a disturbance in the horizontal direction—which is the same direction as the wave propagation—by stretching and then compressing the toy spring.

Tips For Success

Longitudinal waves are sometimes called compression waves or compressional waves , and transverse waves are sometimes called shear waves .

Teacher Demonstration

Transverse and longitudinal waves may be demonstrated in the class using a spring or a toy spring, as shown in the figures.

Waves may be transverse, longitudinal, or a combination of the two . The waves on the strings of musical instruments are transverse (as shown in Figure 13.5 ), and so are electromagnetic waves, such as visible light. Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids.

Sound in solids can be both longitudinal and transverse. Essentially, water waves are also a combination of transverse and longitudinal components, although the simplified water wave illustrated in Figure 13.2 does not show the longitudinal motion of the bird.

Earthquake waves under Earth’s surface have both longitudinal and transverse components as well. The longitudinal waves in an earthquake are called pressure or P-waves, and the transverse waves are called shear or S-waves. These components have important individual characteristics; for example, they propagate at different speeds. Earthquakes also have surface waves that are similar to surface waves on water.

Energy propagates differently in transverse and longitudinal waves. It is important to know the type of the wave in which energy is propagating to understand how it may affect the materials around it.

Watch Physics

Introduction to waves.

This video explains wave propagation in terms of momentum using an example of a wave moving along a rope. It also covers the differences between transverse and longitudinal waves, and between pulse and periodic waves.

• After a compression wave, some molecules move forward temporarily.
• After a compression wave, some molecules move backward temporarily.
• After a compression wave, some molecules move upward temporarily.
• After a compression wave, some molecules move downward temporarily.

Fun In Physics

The physics of surfing.

Many people enjoy surfing in the ocean. For some surfers, the bigger the wave, the better. In one area off the coast of central California, waves can reach heights of up to 50 feet in certain times of the year ( Figure 13.6 ).

How do waves reach such extreme heights? Other than unusual causes, such as when earthquakes produce tsunami waves, most huge waves are caused simply by interactions between the wind and the surface of the water. The wind pushes up against the surface of the water and transfers energy to the water in the process. The stronger the wind, the more energy transferred. As waves start to form, a larger surface area becomes in contact with the wind, and even more energy is transferred from the wind to the water, thus creating higher waves. Intense storms create the fastest winds, kicking up massive waves that travel out from the origin of the storm. Longer-lasting storms and those storms that affect a larger area of the ocean create the biggest waves since they transfer more energy. The cycle of the tides from the Moon’s gravitational pull also plays a small role in creating waves.

Actual ocean waves are more complicated than the idealized model of the simple transverse wave with a perfect sinusoidal shape. Ocean waves are examples of orbital progressive waves , where water particles at the surface follow a circular path from the crest to the trough of the passing wave, then cycle back again to their original position. This cycle repeats with each passing wave.

As waves reach shore, the water depth decreases and the energy of the wave is compressed into a smaller volume. This creates higher waves—an effect known as shoaling .

Since the water particles along the surface move from the crest to the trough, surfers hitch a ride on the cascading water, gliding along the surface. If ocean waves work exactly like the idealized transverse waves, surfing would be much less exciting as it would simply involve standing on a board that bobs up and down in place, just like the seagull in the previous figure.

Additional information and illustrations about the scientific principles behind surfing can be found in the “Using Science to Surf Better!” video.

• The surfer would move side-to-side/back-and-forth vertically with no horizontal motion.
• The surfer would forward and backward horizontally with no vertical motion.

Check Your Understanding

Use these questions to assess students’ achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify such objective and direct them to the relevant content.

• A wave is a force that propagates from the place where it was created.
• A wave is a disturbance that propagates from the place where it was created.
• A wave is matter that provides volume to an object.
• A wave is matter that provides mass to an object.
• No, electromagnetic waves do not require any medium to propagate.
• No, mechanical waves do not require any medium to propagate.
• Yes, both mechanical and electromagnetic waves require a medium to propagate.
• Yes, all transverse waves require a medium to travel.
• A pulse wave is a sudden disturbance with only one wave generated.
• A pulse wave is a sudden disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one wave generated.

What are the categories of mechanical waves based on the type of motion?

• Both transverse and longitudinal waves
• Only longitudinal waves
• Only transverse waves
• Only surface waves

In which direction do the particles of the medium oscillate in a transverse wave?

• Perpendicular to the direction of propagation of the transverse wave
• Parallel to the direction of propagation of the transverse wave

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• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: Physics
• Publication date: Mar 26, 2020
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• Book URL: https://openstax.org/books/physics/pages/1-introduction
• Section URL: https://openstax.org/books/physics/pages/13-1-types-of-waves

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