Can the Doppler Formula be Used for an Accelerated Sound Source?

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    Doppler Formula
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Homework Help Overview

The discussion revolves around the application of the Doppler formula for sound waves when the source is accelerating. Participants are exploring whether the standard formula can be used under these conditions and what implications arise from the acceleration of the source.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the applicability of the Doppler formula for an accelerated source, expressing difficulty in deriving a modified version. Some participants question the validity of using the formula under non-constant relative velocities, while others assert that acceleration does not affect the formula's applicability.

Discussion Status

The discussion is ongoing, with some participants providing insights into the limitations of the Doppler formula when applied to an accelerating source. There is a request for proof regarding the applicability of the formula, indicating a desire for deeper exploration of the topic.

Contextual Notes

Participants are considering the conditions under which the Doppler formula might still hold true despite the acceleration of the source, highlighting the need for clarification on the assumptions involved.

gandharva_23
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Can i use the doppler formula ( i.e f = f(0){(v(+/-)v(0))/(v(+/-)v(s))}) when the source is accelerated taking v as the speed of sound in air v(o) the speed of the observer and v(s) the speed of source at the time the sound wave is generated . I tried deriving this formula but came across some really difficult mathematics in case of an accelerated source ... would be really thankful if someone can derive that formula for an accelerated source or atleast tell whether its applicable or not (in case of an accelerated source ).
 
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gandharva_23 said:
Can i use the doppler formula ( i.e f = f(0){(v(+/-)v(0))/(v(+/-)v(s))}) when the source is accelerated taking v as the speed of sound in air v(o) the speed of the observer and v(s) the speed of source at the time the sound wave is generated .
Yes, the acceleration doesn't affect that formula.
 
can you prove that ?
 
Underlying that doppler formula is an analysis of the time-intervals between successive wavefronts... transmitted by the source and received by the receiver. When the relative velocity is not constant, the formula almost certainly does not strictly apply... but may approximately apply in an appropriate limit.
 
Under what all conditions will it apply ?
 

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