Answer to Question #93762 in Mechanics | Relativity for Simon

Question

Is there a math formula that relates Doppler effect and speed of the moving source? And is it different when applied to sound or when applied to light?

Answer 1

For sound:

$\omega=\omega_0\frac{1+\frac{u}{c}}{1-\frac{v}{c}}$

u — is the receiver velocity relative to the medium.

v — is the wave propagation velocity in the medium.

c — is the wave propagation velocity in the medium.

w_{0 ——} is the source wave frequency.

For light:

$\omega=\omega_0\frac{\sqrt{1-\frac{v^2}{c^2}}}{1+\frac{v}{c}cos\theta}$

c - is the velocity of light.

v - is the source speed relative to receiver.

$\theta$ - is the angle between the direction of the source and the velocity vector associated with the reference frame of the receiver.

w - is the frequency that the receiver will fix.