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Chapter 17 - 17.35

35. (a) The wave speed is given by v = τ/µ ,where τ is the tension in the string and µ is the linear mass

density of the string. Since the mass density is the mass per unit length, µ = M/L ,where M is

the mass of the string and L is its length. Thus

v = τL

(96 . 0 N)(8 . 40 m)

0 . 120 kg

=82 . 0m / s .

(b) The longest possible wavelength λ for a standing wave is related to the length of the string by

L = λ/ 2, so λ =2 L =2(8 . 40 m) = 16 . 8m.

(c) The frequency is f = v/λ =(82 . 0m / s) / (16 . 8m)=4 . 88 Hz.

M =