http://www.ck12.org Chapter 11. Vibrations and Sound
11.2 Wave Speed
Objective
The student will:
- Solve problems involving wavelength, wave speed, and frequency.
Vocabulary
- wave equation:Relates wavelength and wave speed. Distance is speed times time,x=vt, so wavelength is
wave speed times periodλ=vT. - wave speed:How quickly the peak of each wave is moving forward.
The Wave Equation
Simple harmonic motion, moving back and forth in place, has amplitude along with period and frequency. Wave
motion means that the back-and-forth change is also moving through space. This means that there are two further
qualities of a wave.
- The wavelength is the distance between two compressions in the direction of motion of the wave, and is
represented by the Greek letter lambda,λ. For an ocean wave, it would be the distance in meters from the top
of one wave to the next. - Thewave speedis how quickly the peak of each wave is moving forward, and is represented byv(for velocity,
although for our current purpose the direction is not important).
These two are related by the periodTof the wave. The period is the time it takes for a wave to complete one cycle,
which is the time it takes for a peak to move forward one wavelength. Thewave equationexpresses this. Distance
is speed times time, x=vt, so wavelength is wave speed times periodλ=vT.
This can alternately be expressed in terms of frequency. Suppose there are three waves every second. This is
frequencyf= 3 .0 Hz, equivalent to periodT=^13 s. This means that during one second, three waves come out from
the source. Since each peak is one wavelength,λ, ahead of the other, this means that during that one second, the
lead wave has gone ahead three wavelengths. The distance the wave goes in one second is the wave speed. So, the
wave speed is equal to the frequency times the wavelength,v=λf.
Becausef=T^1 , these are mathematically the same:
λ=vT→v=λT=λT^1 =λf
The wave equation says distance wavelength is equal to wave speed multiplied by periodT.