The motors that drive airplane propellers are, in some cases, tuned by using bea

Question

The motors that drive airplane propellers are, in some cases, tuned by using beats. The whirring motor produces a sound wave having the same frequency as the propeller.

Please show work.

Part A
If one single-bladed propeller is turning at 574 rpm and you hear a 2.50 Hz beat when you run the second propeller, what are the two possible frequencies (in rpm) of the second propeller? f1,f2 =

Part B
Suppose you increase the speed of the second propeller slightly and find that the beat frequency changes to 2.60 Hz . In part (A), which of the two answers was the correct one for the frequency of the second single-bladed propeller ?

Part C
How do you know the answer in part (B) to be correct? Explain.

Explanation / Answer

Part A)

First 574 rpm = 9.567 Hz (divide by 60 sec per min)

(9.567 + 2.5)(60) = 724rpm

(9.567 - 2.5)(60) = 424 rpm

Part B)
724 Hz

Part C)

When speeding up the prop, the beat frequency increases, so you are getting farther away from the 574 Hz. Increaseing 724 takes it farther from 574. If we increased 424, we would be getting closer to 574 and thus smaller beat frequency.

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