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Unless indicated otherwise, assume the speed of
Chapter 16, Problem 42E(choose chapter or problem)
Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. Adjusting Airplane Motors. 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 575 rpm and you hear 2.0-Hz 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 2.1 Hz. 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?
Questions & Answers
QUESTION:
Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. Adjusting Airplane Motors. 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 575 rpm and you hear 2.0-Hz 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 2.1 Hz. 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?
ANSWER:Solution 42E Step 1: The speed of sound wave is 344 m/s. The angular frequency of the 1st propeller is, 1 575 rpm = 575 / 60 = 9.58 rotations / s. We know that, = 2 / T And frequency f = 1 / T = 2f ------------------(1) According to this, the frequency of the 1st propeller is, f1= 1 2 = 9.58 / 2 = 1.524 Hz .