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Unformatted text preview: PHYS-408 Fall 2008 Mastering Physics Assignment #7 Solutions Problem 21.11 A 121-cm-long, 4.0 g string oscillates in its m =3 mode with a frequency of 180 Hz and a maximum amplitude of 5.0 mm. (a) What is the wavelength in the string? The first mode for the string would be a half-wavelength. The third mode would be 3/2 wavelengths. So 3 2 = L = 2 3 L = 2 3 121 cm ( ) = 80.7 cm = 0.8067 m (b) What is the tension in the string? The tension is related to the mass density and velocity: v = T s The velocity relates to the wavelength and frequency, which are known. v = f = 0.8067 m ( ) 180 Hz ( ) = 145.2 m / s The linear density is = 4.0 g 121 cm = 4.0 10 3 kg 1.21 m = 3.306 10 3 kg / m So T s = v 2 = 3.306 10 3 kg / m ( ) 145.2 m / s ( ) 2 = 69.7 N Problem 21.12 A heavy piece of hanging sculpture is suspended by a 90-cm-long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz....
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- Spring '08