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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. (a) If one single-bladed propeller is turning at 575rpm and you hear 2Hz beats when you run the second propeller, what are the two possible frequencies (in rpm) of the second propeller? (b) Suppose you increase the speed of the second propeller slightly and find that the beat frequency changes to 2.1Hz. In part (a), which of the two answers was the correct one for the frequency of the second single-bladed propeller? How do you know?

Short Answer

Expert verified

f2 will be either 455rpm or 695rpm.

The correct frequency of the second propeller is f2=695rpm.

Step by step solution

01

Beat frequency formula

The formula to find the beat frequency is fbeat=|f1-f2|.

02

Convert the beat frequency to rpm

Given value of beat frequency is 2Hz. Convert it into rpm.

fbeat=2Hz×60rpm1Hzfbeat=120rpm

03

Calculate the second frequency

Out of two frequencies, one frequency is given, that is, f1=575rpm.

Now, there will be two cases. Eitherf1-f2=120rpm or f1-f2=-120rpm. So, we will get two values of role="math" localid="1664343424560" f2.

  • f2=575rpm-120rpmf2=455rpm
  • f2=575rpm+120rpmf2=695rpm
04

Check the correct frequency

Increasing the speed of the propeller means increasing the f2. In the first case, asf2 increases, the beat frequency decreases. But in the second case, asf2 increases, the beat frequency also increases.

So, the correct frequency of the second propeller is f2=695rpm.

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