University Physics - 13 Edition - Chapter 15 - Problem 22e
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# A piano wire with mass 3.00 g and length 80.0 cm is

University Physics | 13th Edition

Problem 22E

A piano wire with mass 3.00 g and length 80.0 cm is stretched with a tension of 25.0 N. A wave with frequency 120.0 Hz and amplitude 1.6 mm travels along the wire. (a) Calculate the average power carried by the wave. (b) What happens to the average power if the wave amplitude is halved?

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Solution 22E Introduction We have to calculate the average power of the wave on string. Step 1 The average power of wave moving on string is given by 1 2 2 P av= 2 F A The linear mass density of the string is given by The force on the string is F = 25.0 N The frequency of the wave is f = 120.0 Hz Hence the angular frequency = 2f = 2(120.0 Hz) = 754.0 rad/s And the amplitude is A = 1.6 mm = 1.6 × 10m So the average power is 2 3 2 P av= 0.00375 kg/m)(25.0 N)(754.0 rad/s) (1.6 × 10 m) = 0.446 W So the average power carried by the wave is 0.446 W.

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