# PHYS 2211 Module 14 14: Waves

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.

In this module, we study the physics of wave motion. We concentrate on mechanical waves, which are disturbances that move through a medium such as air or water. Like simple harmonic motion studied in the preceding module, the energy transferred through the medium is proportional to the amplitude squared. Surface water waves in the ocean are transverse waves in which the energy of the wave travels horizontally while the water oscillates up and down due to some restoring force. In the picture above, a buoy is used to convert the awesome power of ocean waves into electricity. The up-and-down motion of the buoy generated as the waves pass is converted into rotational motion that turns a rotor in an electric generator. The generator charges batteries, which are in turn used to provide a consistent energy source for the end user. This model was successfully tested by the US Navy in a project to provide power to coastal security networks and was able to provide an average power of 350 W. The buoy survived the difficult ocean environment, including operation off the New Jersey coast through Hurricane Irene in 2011.

The concepts presented in this module will be the foundation for many interesting topics, from the transmission of information to the concepts of quantum mechanics.

Waves are everywhere, although you may never have considered that before. But think about different types of waves. You’ve *heard* of sound waves (pun intended), which involve the vibration of particles like air (if the sound is traveling through air). Also, water waves which are made from water molecules vibrating. Every mechanical wave is produced by some type of particle vibrating.

Even “The Wave” at a stadium can be considered a mechanical wave.

The wave travels through a medium (the people are the particles that make up the medium). What’s important to note here is that the particles move up and down (the people stand and then sit) as the wave pulse travels horizontally. The wave is a disturbance and you can watch this disturbance travel — or propagate — through the medium.

This is how I like to define what a wave is:

A wave is a traveling disturbance that transports energy but not matter.

In this example of a stadium wave, the people sitting on the right don’t move to the seats on the left. The people stay in their same horizontal position. So the wave is not carrying matter with it. But the wave moves horizontally and carries energy (in this case the kinetic energy of the people standing up and sitting down) with it.

We will talk a lot about a wave traveling on a string. The string is the medium and the particles that make up the string are the particles that will vibrate like the people in the stadium wave. Look at this animation to see how, when a wave pulse travels in the string, the particles move up and down while the wave propagates to the right.

This type of wave is called a transverse wave because the particles move perpendicular to the direction that the wave propagates.

Another type of wave is called a longitudinal wave. In this case, the particles vibrate back and forth along the same direction that the wave propagates.

In both types of waves, the wave pulse is a disturbance of the particles from their equilibrium positions. The particles remain very close to the equilibrium position and do not travel with the wave. It is just the disturbance that propagates through the medium.

Here is another animation to show the propagation of a longitudinal wave and a transverse wave:

#### 14.1 Traveling Waves

• 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

#### 14.2 Mathematics of Waves

• Model a wave, moving with a constant wave velocity, with a mathematical expression
• Calculate the velocity and acceleration of the medium
• Show how the velocity of the medium differs from the wave velocity (propagation velocity)

#### 14.3 Wave Speed on a Stretched String

• Determine the factors that affect the speed of a wave on a string
• Write a mathematical expression for the speed of a wave on a string and generalize these concepts for other media

#### 14.4 Energy and Power of a Wave

• Explain how energy travels with a pulse or wave
• Describe, using a mathematical expression, how the energy in a wave depends on the amplitude of the wave

#### 14.5 Interference of Waves

• Explain how mechanical waves are reflected and transmitted at the boundaries of a medium
• Define the terms interference and superposition
• Find the resultant wave of two identical sinusoidal waves that differ only by a phase shift

#### 14.6 Standing Waves and Resonance

• Describe standing waves and explain how they are produced
• Describe the modes of a standing wave on a string
• Provide examples of standing waves beyond the waves on a string