Calculating Frequency Using Doppler Effect in Rotating Speakers

[Knightycloud]

Homework Statement

There is a question asking the frequency of a distant location from two rotating speakers which are attached to the both ends of a meter ruler. The ruler is rotating ar 7 rounds per second and A speaker has a frequency of 500Hz. At the given time they are in a position which is 30⁰ degrees to the horizontal line. How to calculate?

Homework Equations

f'= (V/(V-u₀)f
f = Frequency of a speaker
f' = "to be calculated"
V = Velocity of sound in wind
u₀ = Speed of a speaker

The Attempt at a Solution

u₀ = rω = 0.5 m x 7∏ rad s^-1 = 11 ms^-1


I don't understand how to put the equation when it is not straight to the point. That's where I stuck!

 

[AdrianMay]

There's an ambiguity here: where on the ruler is the pivot? I'll assume it's in the middle. Also, we'll need two answers for the two speakers: one will sound higher and the other lower.

Never mind the equation, work it out this way:

(a) How fast is the speaker moving towards (away from) the listener. We don't care about sideways motion - just the component that's inline with the direction to the listener. For that you'll need to draw a triangle or use some trigonometry. I assume that by 30 degrees you mean the speakers are moving more across you than towards you, but I'm not sure if that's what you mean. Watch out for that ambiguity about where the pivot is.

(b) In the time taken for one cycle of the speaker, how much closer (further away) does the speaker move relative to you.

(c) If you increase or decrease the wavelength by that much, what frequency change is that equivalent to?

Hope that helps.
Adrian.

 

[Knightycloud]

Hm, Thanks. I'll try! :D