Find the expression for the frequency emitted if the source

[grapejellypie]

Homework Statement

A wave source approaches you at constant speed and you measure a wave frequency f1. As the source passes and then recedes, you measure frequency f2. Find the expression for the frequency emitted if the source were stationary in terms of f1, f2, and wave speed v.

Homework Equations

I'm not sure which equations are relevant, but here are some:
f=v/λ (where λ = wavelength)
for situations in which the source is in motion relative to a stationary receiver
fr=(fs)/(1±u/v) where fr=frequency the receiver receives; fs= frequency emitted by source, u=speed of source, and v= wave speed)

The Attempt at a Solution

I'm not sure how to go about solving this problem. I know that the answer will be in terms of variables...
I also know that fs= fr when the source and receiver are stationary

 

[Redbelly98]

... for situations in which the source is in motion relative to a stationary receiver
fr=(fs)/(1±u/v) where fr=frequency the receiver receives; fs= frequency emitted by source, u=speed of source, and v= wave speed)

That's the equation to use here. Plug in the variables for the 2 situations given, to get 2 equations in the 2 "unknowns" fs and u. Ultimately you want an expression for fs that does not contain u.

 

[baba89]

with respect to each other.

I would approach this problem by first understanding the concept of Doppler effect. The Doppler effect is the change in frequency of a wave when the source or observer is in motion relative to each other. In this case, the source is in motion relative to the observer.

To find the expression for the frequency emitted, we can use the Doppler effect equation:

f = f0 * (v + u) / (v + vs)

Where f0 is the frequency emitted by the source when it is stationary, v is the wave speed, u is the speed of the source, and vs is the speed of the observer. In this case, vs is zero as the observer is stationary.

Now, we can substitute the given frequencies f1 and f2 for f0 and solve for fs:

f1 = fs * (v + u) / v
f2 = fs * (v - u) / v

Solving for fs, we get:

fs = f1 * v / (v + u)

or

fs = f2 * v / (v - u)

Therefore, the expression for the frequency emitted by the source when it is stationary is:

fs = (f1 * f2 * v) / (f2 * u + f1 * v)

or

fs = (f1 * f2 * v) / (f1 * u + f2 * v)

I hope this helps in solving the problem.