# Doppler effect and acceleration of source

orangephysik
Homework Statement:
A source at rest is at a distance of s_0 = 1.7 km from you and you measure a frequency of f_0 = 520 Hz. At time t = 0 the source moves directly towards you with a constant acceleration. When the source reaches you, you measure a frequency of f_1 = 1040 Hz.

a) What is the acceleration of the source and at which time t does the source reach you?
Relevant Equations:
Measured frequency, f_Source * = f_0 (1/ (1 - [v_source / v_phasefront] )
Hi. I need help with part a).
I calculated the wavelength of the source by using the formula f_0 = v_phasefront / λ and got λ = (343 m/s) / (520 Hz) = 0.6596 m.
And then I set up an equation for the velocity of the source v(t) = a*t (with v(t = 0 )= 0 m/s) and s(t) = 1/2 * at^2 + s_0. But I just have no idea how I can find the acceleration with these information.

Homework Helper
Homework Statement:: A source at rest is at a distance of s_0 = 1.7 km from you and you measure a frequency of f_0 = 520 Hz. At time t = 0 the source moves directly towards you with a constant acceleration. When the source reaches you, you measure a frequency of f_1 = 1040 Hz.

a) What is the acceleration of the source and at which time t does the source reach you?
Relevant Equations:: Measured frequency, f_Source * = f_0 (1/ (1 - [v_source / v_phasefront] )

Hi. I need help with part a).
I calculated the wavelength of the source by using the formula f_0 = v_phasefront / λ and got λ = (343 m/s) / (520 Hz) = 0.6596 m.
And then I set up an equation for the velocity of the source v(t) = a*t (with v(t = 0 )= 0 m/s) and s(t) = 1/2 * at^2 + s_0.

Hello @orangephysik, ##\qquad## !​

1. I don't think there's anything relativistic about this exercise, but don't mind to be proven wrong.

But I just have no idea how I can find the acceleration with these information.

2. Well, what information haven't you used yet ? Something with Doppler ?

##\ ##

orangephysik
Hello @orangephysik, ##\qquad## !​

1. I don't think there's anything relativistic about this exercise, but don't mind to be proven wrong.

2. Well, what information haven't you used yet ? Something with Doppler ?

##\ ##
I had f_0 = v_phasefront / λ and got λ = (343 m/s) / (520 Hz) = 0.6596 m, and this is the wavelength of the source when it was at rest.
With the same formula, f_1 = v_phasefront / λ' , so λ' = (343 m/s) / (1040 Hz) = 0.3298 m, this is the wavelength when the source reaches me.

Now using
Measured frequency, f_Source * = f_0 (1/ (1 - [v_source / v_phasefront] )

1040 Hz = 520 Hz * (1/ [1 - (v_source / 343 m/s) ]), rearranging I got v_source = 171.5 m/s.

I also know λ' = λ - v_source * T (whereby T is the period). Plugging in the values to find T, I got T = 1.923 ms.

So the acceleration must be a = v_source / T = 8.92*10^4 m/(s^2). Is this the correct way of solving the question?

Homework Helper
Is this the correct way of solving the question?
Actually there are two questions. One is asking for the acceleration of the source, the other for a time.
I agree the first step is to find the final speed of the source. Looks OK.
But then you derive a T in a cumbersome way (it is 1/520) and you seem to think this period is equal to the time the source needs to reach you. Why ? 2 ms to cover what distance again ?

The equations you set up at the end of post #1 look a lot more promising to me !

##\ ##

orangephysik
Actually there are two questions. One is asking for the acceleration of the source, the other for a time.
I agree the first step is to find the final speed of the source. Looks OK.
But then you derive a T in a cumbersome way (it is 1/520) and you seem to think this period is equal to the time the source needs to reach you. Why ? 2 ms to cover what distance again ?

The equations you set up at the end of post #1 look a lot more promising to me !

##\ ##
Oh right. The period T is the time it takes for the sound waves to travel a distance of λ - λ' = 0.3298 m.

So since acceleration is a = Δv/Δt, I already have Δv since v_0 = 0 m/s and now I just need Δt. But the question implies that I can find the acceleration without knowing Δt.

I have v(t) = a*t ⇔ 171.5 m/s = a*t ⇔ t = (171.5 m/s) / a (whereby t is the time it takes to reach me, since 171.5 m/s is the speed when it reaches me)

I also have s(t) = 1/2 * at2
I know that it has travelled 1.7 km when it reaches me, so 1.7 km = 1/2 * at2
⇔ t = √[(3.4 km)/a]

Setting these two equations for t equal, I get a = 8.65 m/s, which means t = 19.83 s.

I hope this time I'm right Hoping you're right is one thing. What is needed to convince you that you are right ?
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