The Doppler Effect: Deducing an Expression for Frequency

[jono90one]

Homework Statement

A sound source moves at a constant velocity. A listener is standing at a distance L away from it. Given that the source moves in a straight line at a right angle to the listener and starts closest to the listener (ie at t=0) deduce an expression for the frequency heard by the listener in relation to time.

Homework Equations

f_l=f_s(v/(v-v_s))
where l is listener and s is source

The Attempt at a Solution

It's obviously Doppler effect related.
So far I’ve done T=1/f_s
And gotten
f_l=v/T(v-v_s)

But unsure how to get L into the equation.
Surely VT is the distance traveled by the wave and v_sT is λ_s. Is there any orientation where L can be introduced? Or is this version correct?

 

[abhishek ghos]

take in the velocity component of the source away from the observer at each instant of time in the governing equation.

 

[jono90one]

(edit) So you mean f=v/T(vs-v)??

 

[abhishek ghos]

No
O(t=0)----------------------->vt(point A)(source)
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Point B(you)
I want you to find the component of source’s(A) velocity
Along the line joining point A & point B at an instant t
And plug that velocity into your equation for vs.