How Does Acceleration Affect the Frequency of Sound Heard by an Observer?

[ambuj123]

I have this problem which is really bugging me if someone could help me i would be very grateful.
Q. A source emmiting sound of frequency v is placed at a large distance from an observer source starts moving towards observer with uniform acceleration a find frequency heard by observer corresponding to wave emmited just after the source starts. The spped in medium is s
Answer: (2sv^2/2sv-a)
thank you
Ambuj

 

[Parth Dave]

basically, the question is asking you to derive the doppler effect formula (there are a couple versions, and i haven't seen this one before). Start by looking at the wavelength and determine what would happen if the source starts moving towards the observer. Can you find out how to account for the changes? Remember that the speed of sound is constant, so see what that change in wavelength does to the frequency. Try it out, if you get stuck than post where. But you've given very little info as to what you actually did. Let us know where you are having problems so we know how to help.

 

[ambuj123]

Thanx

Was able to solve the problem
but if yould see the solution and advice would be nice.
Here is attached solution scanned to jpg compressed in zip

:surprise:

 

[himanshu121]

It little bit hazy over scanned jpg Anyway u can check it

Let source is at S₁ initially and emits wavefront W₁
Since Source is accelerating let the other position be S₂. Where it emits W₂

now
$$\Delta (W_1W_2) = \lambda ' = v_s t - \frac{at^2}{2}$$
f(apparent) = $$\frac{ v_s}{\lambda '}$$
Also,

$$t=\frac{1}{f_0}$$

I believe that's what u have done Still u can Read more thoroughly about Doppler Effect from Resnik And Halliday(Nicely Given)