Find the frequency of a wave with whose wavelength is 5 meters and which propagates at the velocity of 30 meters/second.
Visualize a 1-second section of the wave. It is 30 meters long, with peaks 5 meters apart. This 1-second section therefore contains 30 meters / ( 5 meters / peak) = 6 peaks.
In 1 second, therefore, these 6 peaks will pass.
We call the quantity 6 peaks / second the frequency of the wave.
Frequency is measured in peaks/second, or, since a peak occurs once per cycle of the wave, in cycles/second. The unit cycles/second is also called the 'Hertz', abbreviated Hz (for a guy named Hertz who had a lot to do with developing wave theories).
If a wave passes at velocity v with wavelength `lambda, then in time interval `dt, a wave segment of length v `dt will pass.
With distance `lambda between peaks, the number of peaks passing in this time interval is n = v `dt / `lambda.
The number of peaks per unit of time is thus
The figure below shows the distance moved in time `dt by a wave with velocity v, and the wavelength `lambda, or distance between peaks. We see that the number of peaks in time `dt is equal to the distance traveled in this time, divided by the distance between consecutive peaks, or v `dt / `lambda. The frequency is the number of peaks divided by the time `dt, or [ v `dt / lambda ] / `dt = v / `lambda.
"