Calculating Frequency Difference of a Rotating Siren - How Fast Must It Spin?

AI Thread Summary
To calculate the frequency difference perceived by an observer from a rotating siren, the disk must spin at a specific tangential velocity. The observer perceives two frequencies differing by 50 Hz when the disk's rotation is factored in, indicating that the source is indeed moving. The relevant equations involve angular velocity and tangential velocity, with the relationship Vt = ω * r being crucial. The challenge lies in applying these formulas correctly to derive the necessary speed from the given frequency and radius. Understanding the impact of the disk's tilt on frequency difference also requires considering the vector nature of velocity.
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Homework Statement


A siren has two loud speakers attached to a rotating disk. The disks radius is 3m. The speakers emit a sound frequency of 300 Hz.(Speed of sound in air is 344 m/s)
A)How fast does the disk need to spin for an observer standing some distance away to perceive two frequencies that are different by by 50 Hz.
B)Whats the difference of the two frequencies if the disk is tilted by 50 degrees?(Hint: velocity is a vector)

Homework Equations




The Attempt at a Solution


Please help me get started. I'm assuming its both stationary observer and source but i don't know how to implement a rotation siren. Does that mean the source is actually moving?
 
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Yes, the siren is actually moving. What's the tangential velocity of a rotating disk?
 
Well that's Vt=w*r, but i don't see how you obtain that from given just frequency and radius. Is their a formula that that will help get me started.
Heres some formulas including w.
k=w/v
w=2*pi/T
But none of these help, yet atleast
 
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