MadSci Network: Physics

Re: Computer simulation [algorthym ] of the doppler effect for sound?

Date: Tue Aug 24 17:03:20 1999
Posted By: Stephen Murray, Physicist
Area of science: Physics
ID: 934808620.Ph

At the risk of boring you with information that you already know, the Doppler shift for sound is given by a fairly simple formula, so long as the motions of the source and observer are below the speed of sound. As given in the 3rd edition of "Physics," by Halliday and Resnick (and probably also in the chapter on sound waves in the current edition of Halliday, Resnick & Walker), the relation between the observed and emitted frequencies of sound waves is:

f_obs=f_emitted * (V +/- V_o) / (V -/+ V_s)

In the above equation, V is the speed of sound, V_o is the motion of the observer towards or away from the source, and V_s is the motion of the source toward or away from the observer. In using the +/- and -/+, the first (+ and -) operator is to be used if the motion involved is towards the source or observer, while the second operator (- and +) is to be used if the motion is away from either the source or observer.

The equation simplifies much more if the motions are much less than the speed of sound. Then, you can simply write:

f_obs=f_emitted * (1 +/- u/V)

Here, u is the *relative* motion of the source and observer. The plus sign is used for motions where the observer and source approach each other, and the minus sign applies if they are moving apart.

To apply this in a program to demonstrate the Doppler shift is really an exercise in computer programming. It would be system-dependent, but in principle fairly simple to have the computer output sound of a given frequency, set by a pre-determined emitted frequency (or spectrum), and a relative motion of source and observer. It could even be linked to an animation, using Java applets, such as the physlets developed at Davidson College (I'm thinking here more in terms of a lecture demonstration, or distance education tool).

With that said, however, I don't know of any particular applications that do all of this. It may be so simple to do, that many have done it independently.

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