Is Doppler Effect Infinite when Wave Velocity Equals Emitter Velocity?

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SUMMARY

The discussion centers on the Doppler Effect, specifically addressing the scenario where the wave velocity equals the emitter velocity. It is established that when the emitter travels at the speed of sound, the emitted waves travel alongside the emitter, resulting in a theoretical wavelength of zero and an infinite frequency (f). This phenomenon explains the sonic boom experienced when a jet reaches sound speed. Additionally, participants inquire about the demonstration of the Doppler-Fizeau formula, suggesting that it can be adapted for nonrelativistic cases by substituting the speed of light with the speed of sound.

PREREQUISITES
  • Understanding of the Doppler Effect and its mathematical representation.
  • Familiarity with the Doppler-Fizeau formula in electrodynamics.
  • Basic knowledge of wave mechanics and sound propagation.
  • Concept of frequency and wavelength in wave theory.
NEXT STEPS
  • Research the derivation of the Doppler-Fizeau formula in electrodynamics.
  • Explore nonrelativistic approximations of the Doppler Effect.
  • Study the implications of sonic booms in aerodynamics.
  • Investigate the relationship between wave velocity and emitter velocity in various mediums.
USEFUL FOR

Physicists, acoustics engineers, students studying wave mechanics, and anyone interested in the applications of the Doppler Effect in real-world scenarios.

Raparicio
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Hello.

I have a question on Doppler effect. When the wave has the same velocity that the emisor, u have this:

f= \frac {\partial {(Vs-Vo)}} {\partial {(Vs-Ve)}} f'

In this case, Vs=Ve, f=infinite?
 
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Theoretically, yes. When the emitter travels at the speed of sound, the emitted waves travel along with the emitter and therefore the wavelength will go to zero. So f = Vs/wavelength goes to infinity. That's why you here a blast when a jet reaches sound speed.
 
d

Timbuqtu said:
Theoretically, yes. When the emitter travels at the speed of sound, the emitted waves travel along with the emitter and therefore the wavelength will go to zero. So f = Vs/wavelength goes to infinity. That's why you here a blast when a jet reaches sound speed.

Where can i find the demonstration of doppler formula?
 
There's an elegant proof for the Doppler-Fizeau formula in electrodynamics books.I'm sure that setting "c"----"v_{sound}" & making approximations u can find the nonrelativistic cases...All 4 of them (in the case of leght,there are only 2).

Daniel.
 
dextercioby said:
There's an elegant proof for the Doppler-Fizeau formula in electrodynamics books.I'm sure that setting "c"----"v_{sound}" & making approximations u can find the nonrelativistic cases...All 4 of them (in the case of leght,there are only 2).

Daniel.

Dear Dextercious:

I don't understand this "I'm sure that setting "c"----"v_{sound}" & making approximations".

Setting where?
 
In the general Doppler-Fizeau formula...

Daniel.
 

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