P18_041 - 41. The string is fixed at both ends so the...

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Unformatted text preview: 41. The string is fixed at both ends so the resonant wavelengths are given by λ = 2L/n, where L is the length of the string and n is an integer. The resonant frequencies are given by f = v/λ = nv/2L, where v is the wave speed on the string. Now v = τ /µ, where τ is the tension in the string and µ is the linear mass density of the string. Thus f = (n/2L) τ /µ. Suppose the lower frequency is associated with n = n1 and the higher frequency is associated with n = n1 + 1. There are no resonant frequencies between so you know that the integers associated with the given frequencies differ by 1. Thus f1 = (n1 /2L) τ /µ and n1 + 1 τ 1 n1 1 τ τ τ f2 = = + = f1 + . 2L µ 2L µ 2L µ 2L µ This means f2 − f1 = (1/2L) τ /µ and τ = = = 4L2 µ(f2 − f1 )2 4(0.300 m)2 (0.650 × 10−3 kg/m)(1320 Hz − 880 Hz)2 45.3 N . ...
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