PS-7.3 Summarize characteristics of waves (including displacement, frequency, period, amplitude, wavelength, and velocity as well as the relationships among these characteristics).
Frequency - hertz
Wave properties: period, amplitude, wavelength, velocity
The amplitude of a transverse wave is referred to as wave height. Amplitude is a measure of the energy a wave is carrying. In diagram "A" below, the red line is the resting point or " equilibrium position" of the wave. If the wave had zero energy, then it would be just a flat line and would have no height. The higher the wave is above the equilibrium position the greater the amplitude, and the greater the amplitude, the greater the energy of the wave. In other words, wave energy is proportional to wave amplitude.
The amplitude of a longitudinal wave is analogous to the degree of compression. The more compressed the compressions are, the greater the amplitude. This is illustrated below in diagram "C".
The frequency of the wave is the number of complete waves or vibrations generated per second. Frequency is measured waves per second or Hertz. 1 Hertz is equal to one wave or cycle per second. One way to think about frequency is to imagine a wave passing you. If 5 complete waves pass in one second then the frequency of the wave is 5 waves per second or 5Hertz. Since frequency depends on the number of waves that pass a point in one second it stands to reason that, if the wave speed is constant, the shorter the wavelength the higher the frequency. In other words, the frequency of a wave is inversely related to the wavelength. The longer the wavelength, the fewer waves will pass a given point in one second, and the lower the frequency.
Click here to view a video that illustrates the inverse relationship between wavelength and frequency. When you watch the video note that the high frequency, short wavelength wave is the bottom wave and the low frequency, long wavelength is on the top. Remember: When the frequency gets greater the wavelength get shorter.
Diagram "D" illustrates this inverse relationship for a pair of transverse waves.
Here is a similar diagram that illustrates the inverse relationship between wavelength and frequency for a longitudinal wave. In the diagram "C" stands for compression and "R" stands for rarefaction.
The period of a wave is the time for one cycle (or vibration) or the time for one complete wave to pass a given point. The period of a wave is measured in seconds or seconds per wave. One way to visualize the period of a wave is to imagine the wave crests or wave compressions as soldiers marching along a road. If the time between soldiers is 2.0s then the period is 2.0s. The period of a wave and its frequency are inverses of each other. This is easily seen in the fact that frequency is measured in waves per second and wave period is measured in seconds per wave. These two statements are inverses of each other. Mathematically this relationship appears like this:
f=1/T and T=1/f where "f" is frequency and "T" is the period of the wave.
This relationship can be used in the following manner:
Q: What is the frequency of a wave that has a period of .04s? The answer is quite simple to determine, just find the inverse of .4s. 1 /.4s = 2.5Hz
Q2: What is the period of a wave that has a frequency of 2500Hz? Again, the answer is easy to determine. Just find the inverse of 2500Hz. 1/2500Hz = 4 x 10-4s or .0004s
The velocity of the wave depends on the type of wave and the type of medium through which the wave is traveling. The velocity of a wave will not change UNLESS the characteristics of the medium or type of wave changes. This is clearly illustrated by looking at the effect that air temperature has on the speed of sound. The actual speed of sound is 331.4 m/s at 0oC and this speed increases by 0.6 m/s for each degree Celsius above zero.
Changes in wave frequency or wavelength do not affect the velocity of mechanical waves. Remember that there is an inverse relationship between wavelength and wave frequency. This means that a increase in wavelength will produce an equal decrease in wave frequency. The wave velocity, which is the product of wavelength and frequency will remain constant.
Click here to see a table of the speed of sound in different materials. The information is from Gundersen's
The Handy Physics Answer Book