Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo

Learning Objectives

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

  • State the characteristics of a wave.
  • Calculate the velocity of wave propagation.
There is a high tidal wave of about 10 feet high in a sea. Three boats carrying three four persons each are ahead of the wave, which is coming toward them.
Figure 16.27 Waves in the ocean behave similarly to all other types of waves. (credit: Steve Jurveston, Flickr)

What do we mean when we say something is a wave? The most intuitive and easiest wave to imagine is the familiar water wave. More precisely, a wave is a disturbance that propagates, or moves from the place it was created. For water waves, the disturbance is in 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. For earthquakes, there are several types of disturbances, including disturbance of Earth’s surface and pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Visualizing water waves is useful because there is more to it than just a mental image. Water waves exhibit characteristics common to all waves, such as amplitude, period, frequency and energy. All wave characteristics can be described by a small set of underlying principles.

A wave is a disturbance that propagates, or moves from the place it was created. The simplest waves repeat themselves for several cycles and are associated with simple harmonic motion. Let us start by considering the simplified water wave in Figure 16.28. The wave is an up and down disturbance of the water surface. It causes a sea gull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The time for one complete up and down motion is the wave’s period TT. The wave’s frequency is f=1/Tf=1/T, as usual. The wave itself moves to the right in the figure. This movement of the wave is actually the disturbance moving to the right, not the water itself (or the bird would move to the right). We define wave velocity vwvw to be the speed at which the disturbance moves. Wave velocity is sometimes also called the propagation velocity or propagation speed, because the disturbance propagates from one location to another.

Misconception Alert

Many people think that water waves push water from one direction to another. In fact, the particles of water tend to stay in one location, save for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water stays in one place. If you feel yourself pushed in an ocean, what you feel is the energy of the wave, not a rush of water.

The figure shows an idealized ocean wave with two crests and two troughs that passes under a sea gull that bobs up and down in simple harmonic motion. The wave has a wavelength lambda which is the distance between adjacent identical parts of the wave. The height of a crest is equal to the depth of the trough that is X, therefore the total vertical distance between the top of a crest and the bottom of the trough is two-X.
Figure 16.28 An idealized ocean wave passes under a sea gull that bobs up and down in simple harmonic motion. The wave has a wavelength λλ, which is the distance between adjacent identical parts of the wave. The up and down disturbance of the surface propagates parallel to the surface at a speed vwvw.

The water wave in the figure also has a length associated with it, called its wavelength λ λ , the distance between adjacent identical parts of a wave. (λλ is the distance parallel to the direction of propagation.) The speed of propagation vwvw is the distance the wave travels in a given time, which is one wavelength in the time of one period. In equation form, that is

v w = λ T v w = λ T


v w = . v w = .

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

Take-Home Experiment: Waves in a Bowl

Fill a large bowl or basin with water and wait for the water to settle so there are no ripples. Gently drop a cork into the middle of the bowl. Estimate the wavelength and period of oscillation of the water wave that propagates away from the cork. Remove the cork from the bowl and wait for the water to settle again. Gently drop the cork at a height that is different from the first drop. Does the wavelength depend upon how high above the water the cork is dropped?

Example 16.8

Calculate the Velocity of Wave Propagation: Gull in the Ocean

Calculate the wave velocity of the ocean wave in Figure 16.28 if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.


We are asked to find vwvw. The given information tells us that λ=10.0mλ=10.0m and T=5.00sT=5.00s. Therefore, we can use v w = λ T v w = λ T to find the wave velocity.


  1. Enter the known values into vw=λTvw=λT:
    v w = 10.0 m 5 .00 s . v w = 10.0 m 5 .00 s .
  2. Solve for vwvw to find vw= 2.00 m/s.vw= 2.00 m/s.


This slow speed seems reasonable for an ocean wave. Note that the wave moves to the right in the figure at this speed, not the varying speed at which the sea gull moves up and down.

Transverse and Longitudinal Waves

A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in Figure 16.29 propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave or shear wave; in such a wave, the disturbance 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 16.30 shows an example of a longitudinal wave. The size of the disturbance is its amplitude X and is completely independent of the speed of propagation vwvw.

The figure shows a woman holding a long spring in her hand and moving it up and down causing it to move in a zigzag manner away from her. It is an example of a transverse wave, the wave propagates horizontally. The direction of motion of the wave is shown with the help of right arrows at each crest and trough.
Figure 16.29 In this example of a transverse wave, the wave propagates horizontally, and the disturbance in the cord is in the vertical direction.
The figure shows a woman standing at left pushing a long spring in to and fro motion in horizontal direction away from her without moving her hand up and down. The cord stretches and contracts back and forth. This is an example of a longitudinal wave, the wave propagates horizontally. At some points the spring is compressed and at some other points the spring is expanded. One contracted part is equal to the amplitude X.
Figure 16.30 In this example of a longitudinal wave, the wave propagates horizontally, and the disturbance in the cord is also in the horizontal direction.

Waves may be transverse, longitudinal, or a combination of the two. (Water waves are actually a combination of transverse and longitudinal. The simplified water wave illustrated in Figure 16.28 shows no longitudinal motion of the bird.) The waves on the strings of musical instruments are transverse—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. Fluids do not have appreciable shear strength, and thus the sound waves in them must be longitudinal or compressional. Sound in solids can be both longitudinal and transverse.

The figure shows a guitar connected to an amplifier and a man holding a sheet of paper facing the speaker attached to the amplifier. The strings of the guitar when played cause transverse waves. On the other hand, the sound of the guitar creates ripples on the sheet of paper causing it to rattle in a direction that shows that the sound waves are longitudinal.
Figure 16.31 The wave on a guitar string is transverse. The sound wave rattles a sheet of paper in a direction that shows the sound wave is longitudinal.

Earthquake waves under Earth’s surface also have both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). These components have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water.

Check Your Understanding

Why is it important to differentiate between longitudinal and transverse waves?

PhET Explorations

Wave on a String

Watch a string vibrate in slow motion. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator. Adjust the damping and tension. The end can be fixed, loose, or open.

Order a print copy

As an Amazon Associate we earn from qualifying purchases.


This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information Citation information

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.