# Waves and Their Properties

## Wave Properties: Speed, Amplitude, Frequency, and Period


### Section Key Terms


### Wave Variables

In the chapter on motion in two dimensions, we defined the following variables to describe harmonic motion:
1. Amplitude—maximum displacement from the equilibrium position of an object oscillating around such equilibrium position
2. Frequency—number of events per unit of time
3. Period—time it takes to complete one oscillation
For waves, these variables have the same basic meaning. However, it is helpful to word the definitions in a more specific way that applies directly to waves:
1. Amplitude—distance between the resting position and the maximum displacement of the wave
2. Frequency—number of waves passing by a specific point per second
3. Period—time it takes for one wave cycle to complete
In addition to amplitude, frequency, and period, their wavelength and wave velocity also characterize waves. The wavelength  
   is the distance between adjacent identical parts of a wave, parallel to the direction of propagation. The wave velocity  
   is the speed at which the disturbance moves.
Consider the periodic water wave in . Its wavelength is the distance from crest to crest or from trough to trough. The wavelength can also be thought of as the distance a wave has traveled after one complete cycle—or one period. The time for one complete up-and-down motion is the simple water wave’s period T. In the figure, the wave itself moves to the right with a wave velocity vw. Its amplitude X is the distance between the resting position and the maximum displacement—either the crest or the trough—of the wave. It is important to note that this movement of the wave is actually the disturbance moving to the right, not the water itself; otherwise, the bird would move to the right. Instead, the seagull bobs up and down in place as waves pass underneath, traveling a total distance of 2X in one cycle. However, as mentioned in the text feature on surfing, actual ocean waves are more complex than this simplified example.

### The Relationship between Wave Frequency, Period, Wavelength, and Velocity

Since wave frequency is the number of waves per second, and the period is essentially the number of seconds per wave, the relationship between frequency and period is
or
just as in the case of harmonic motion of an object. We can see from this relationship that a higher frequency means a shorter period. Recall that the unit for frequency is hertz (Hz), and that 1 Hz is one cycle—or one wave—per second.
The speed of propagation vw is the distance the wave travels in a given time, which is one wavelength in a time of one period. In equation form, it is written as
or
From this relationship, we see that in a medium where vw is constant, the higher the frequency, the smaller the wavelength. See .
These fundamental relationships hold true for all types of waves. As an example, for water waves, vw is the speed of a surface wave; for sound, vw is the speed of sound; and for visible light, vw is the speed of light. The amplitude X is completely independent of the speed of propagation vw and depends only on the amount of energy in the wave.

### Solving Wave Problems


### Practice Problems


### Check Your Understanding


### Section Summary

1. A wave is a disturbance that moves from the point of creation at a wave velocity vw.
2. A wave has a wavelength  
 , which is the distance between adjacent identical parts of the wave.
3. The wave velocity and the wavelength are related to the wave’s frequency and period by  
   or  
  
4. The time for one complete wave cycle is the period T.
5. The number of waves per unit time is the frequency ƒ.
6. The wave frequency and the period are inversely related to one another.

### Key Equations


### Concept Items


### Critical Thinking


### Problems


### Test Prep Multiple Choice


### Test Prep Short Answer


### Test Prep Extended Response
