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

[gandharva_23]

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 ).

 

[Meir Achuz]

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.

 

[gandharva_23]

can you prove that ?

 

[robphy]

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.

 

[gandharva_23]

Under what all conditions will it apply ?