# Shock wave's frequency

1. Sep 25, 2005

### brasilr9

Is the frequency of the shock waves detected by the observer infinte?
And, as I know, a shock wave can be produced even if the source didn't emit sound waves. When a object moving in a medium at a speed faster than the speed of medium's elastic wave's speed. In this case how we calculate the wave's frequency?

2. Sep 26, 2005

### shyboy

well, the shock wave hits only once so yes, the frequency is infinitely small. On the other hand, the detected frequency from the source is finite, but Doppler shifted to a lower value.
For example, if source is just "beeping", you will still hear the beeps after it will pass you, but the interval between beeps will be bigger.

3. Sep 26, 2005

### pervect

Staff Emeritus
The only wave that has a single frequency is a sine wave.

Mathematically, the spectrum of a wave is usually defined by its fourier transform. The fourier transform takes a functio from the "time domain" to the "frequency domain". The magnitude of the fourier transform at a specific frequency band can be interpreted as how much of the energy of the wave lies within that band. For a detailed defintion, see the wikipedea article

http://en.wikipedia.org/wiki/Continuous_Fourier_transform

The fourier transform you are probably interested in to represent a shock wave is the last entry in the Wikipedia table, the "Heavside step function".

At any frequncy other than 0, the magnitude of the fourier transform is 1/w - the magnitude decreases with frequency but never drops to zero,.

This is an idealization, real shock waves do not actually have infinitely fast rise-times.

4. Sep 27, 2005