Shock Wave Frequency: Observer, Emission & Calculation

[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?

Thanks for answering my question!

 

[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.

 

[pervect]

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?

Thanks for answering my question!

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 into 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.

 

[brasilr9]

thanks for answering my question.