The drawing shows a 12.0 kg ball being swirled around in acircular path on the e

Question

The drawing shows a 12.0 kg ball being swirled around in acircular path on the end of a string. The motion occurs on africtionless, horizontal table. The angular speed of the ball is15rad/sec. The string has a mass of .030kg.

b) The ball is designed to whistle has it is swung in thecircle. It whistles as a frequency of 10 kHz. Assume the speed ofsound in air is 343 m/s and the length of the string is 1.25 m.Determine:

- the frequency that observer 1 hears when the ball is atposition A

- the frequency that observer 1 hears when the ball is atposition B

- the frequency that observer 3 hears when the ball is atposition A

Explanation / Answer

The mass of the ball is m = 12.0 kg being swirled around in acircular path on the end of a string. The angular speed of the ball is w = 15 rad/sec The ball whistles at a frequency of f = 10 kHz = 10 *103 Hz The speed of sound in air is vsnd= 343 m/s The length of the string is l = 1.25 m At point A,the source (ball) is moving toward the observer1,therefore,the frequency that observer 1 hears when the ball is atposition A is f1= f * (vsnd +vobs/vsnd - vsource)------------------(1) Here,vsource= l * w = 1.25 * 15 = 18.75 m/s andvobs= 150 m/s Substituting the values in equation (1),we get f1= 10 * 103 * (343 + 150/343 -18.75) or f1= 15.2 * 103 Hz = 15.2kHz The frequency that observer 1 hears when the ball is atposition B is f2= f * (vsnd -vobs/vsnd + vsource) or f2= 10 * 103 * (343 -150/343 + 18.75) or f2= 5.33 * 103 Hz = 5.33kHz The frequency that observer 3 hears when the ball is atposition A is f3= f * (vsnd +vobs/vsnd - vsource) Here,vobs= 25 m/s and vsource= 18.75m/s or f3= 10 * 103 * (343 + 25/343 -18.75) or f3= 11.35 * 103 Hz or f3= 11.35 kHz The frequency that observer 3 hears when the ball is atposition B is f4= f * (vsnd -vobs/vsnd + vsource) or f4= 10 * 103 * (343 -25/343 + 18.75) or f4= 8.79 * 103 Hz = 8.79 kHz The frequency that observer 3 hears when the ball is atposition B is f4= f * (vsnd -vobs/vsnd + vsource) or f4= 10 * 103 * (343 -25/343 + 18.75) or f4= 8.79 * 103 Hz = 8.79 kHz

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