Swinging fans & Doppler's shift

[TharitTk]

Homework Statement

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Homework Equations

The Attempt at a Solution

I consider that if the fan is swinging, the source of sound (fan) will have an speed that lead to doppler's shift.
but i can't calculate for this. i think speed of source will be ωR cos (ωt) (R is the radius of fan's swinging) but there is no data of R . I only know that in question 3 will answer nearly constant with time becuse source of sound will be a spot and we neglet the speed from swinging.

 

[theodoros.mihos]

I am not sure. What change on the wave solution:

$$ A(x,t) = A\sin(\omega{t}-kx) $$

by wind speed, $\omega$ or $k$?

 

[haruspex]

The flow of air makes this a tricky question. If you think of the wave fronts leaving the wire cage, they get carried by the flow of air as well as traveling through it. Consider a wavefront generated at time t, in some parcel of air P that comes through the wire. The wavefront's arc will continue to be centred on P as P moves. Thus, when it reaches the listener, it will be as though it has come from where P now is.
If the listener is at distance D from the fan (large compared with fan size), how long does it take for the sound to reach the listener? Where will the corresponding apparent source be then? How fast will the apparent source be moving towards or away from the listener (it will depend on the fan angle)?