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

In summary, the Doppler formula (f = f(0){(v(+/-)v(0))/(v(+/-)v(s))}) can still be used when the source is accelerated, with the speed of sound in air (v), the speed of the observer (v(o)), and the speed of the source (v(s)) at the time the sound wave is generated. While the formula may not strictly apply when the relative velocity is not constant, it can still be used as an approximation in certain cases. The applicability of the formula depends on the analysis of time-intervals between successive wavefronts transmitted by the source and received by the receiver.
  • #1
gandharva_23
61
0
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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  • #2
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.
 
  • #3
can you prove that ?
 
  • #4
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.
 
  • #5
Under what all conditions will it apply ?
 

1. What is the Doppler formula and how does it work?

The Doppler formula, also known as the Doppler effect, is a physical phenomenon that explains the change in frequency of waves (such as sound or light) when the source of the waves is in motion relative to an observer. This means that the frequency of the waves will appear higher when the source is moving towards the observer and lower when the source is moving away from the observer.

2. What causes problems with the Doppler formula?

The Doppler formula assumes that the source of the waves and the observer are not moving relative to each other. However, in real-world scenarios, this is usually not the case. For example, if the source of the waves is moving at a high speed or the observer is also in motion, the Doppler formula may not accurately predict the change in frequency.

3. How do you calculate the Doppler effect for a moving source or observer?

The formula for calculating the Doppler effect in the case of a moving source or observer is slightly different than the standard formula. It takes into account the velocities of both the source and the observer, as well as the speed of the wave. This can be calculated using the following equation: Δf/f = v/c * (cosθ ± v/c), where v is the velocity of the source or observer, c is the speed of the wave, and θ is the angle between the direction of motion and the direction of the wave.

4. How accurate is the Doppler formula in real-world scenarios?

The accuracy of the Doppler formula depends on the specific conditions of the scenario. In some cases, the formula may provide a close approximation of the actual frequency shift, while in other cases it may be significantly off. For example, the formula may be less accurate for objects moving at very high speeds or for waves with very high frequencies. In general, it is best to use caution when applying the Doppler formula to real-world situations and to consider other factors that may affect the frequency shift.

5. Can the Doppler effect be observed in everyday life?

Yes, the Doppler effect can be observed in many aspects of everyday life. For example, the change in pitch of a siren as an ambulance or police car passes by is a result of the Doppler effect. It can also be observed in the redshift of light from distant galaxies, the change in frequency of radio waves from moving objects, and even the change in frequency of sound when a car passes by on the street.

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