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

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SUMMARY

The discussion centers on calculating the required rotational speed of a siren's disk to create a frequency difference of 50 Hz for an observer. Given a disk radius of 3 meters and a sound frequency of 300 Hz, the necessary tangential velocity can be derived using the Doppler effect principles. The speaker's sound frequency and the speed of sound in air (344 m/s) are critical for these calculations. Additionally, the impact of tilting the disk by 50 degrees on frequency differences is also explored.

PREREQUISITES
  • Understanding of the Doppler effect in sound waves
  • Familiarity with angular velocity and tangential velocity calculations
  • Basic knowledge of trigonometry for angle adjustments
  • Proficiency in using formulas related to wave frequency and speed
NEXT STEPS
  • Calculate the tangential velocity required for a 50 Hz frequency difference using the Doppler effect
  • Explore the effects of angular displacement on frequency perception
  • Study the relationship between frequency, wavelength, and speed of sound in different mediums
  • Investigate the mathematical modeling of rotating systems in physics
USEFUL FOR

Physics students, acoustics engineers, and anyone interested in sound wave behavior and rotational dynamics will benefit from this discussion.

sirclash
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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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