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One string of a certain musical instrument is 80.0 cm long and has a mass of...

One string of a certain musical instrument is 80.0 cm long and has a mass of 8.79 g . It is being played in a room where the speed of sound is 344 m/s.

To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.756 m ? (Assume that the breaking stress of the wire is very large and isn’t exceeded.)

What frequency sound does this string produce in its fundamental mode of vibration?

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Answer #1

Frequency wanted is 344 / 0.756 = about 455 Hz

Wavelength of the 2nd overtone is 2 * 0.8 / 3 = 0.534 m

If the frequency is 455 Hz ( are you sure about that wavelength ?) then

v = 455 * 0.53 = 242.97 m/s

V^2 = T / (m/l)

T = 59.03 * 10^3 * (8.79/.8) * 10^-3 = 650 N

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