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Question

A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m1 kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2.0 m long portion of the string.

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Solution

A=1mm=103m,

m=6g/m=6×103kg/m

T = 60 N, f = 200 Hz

V=(Tm)=(60)(6×103)=102=100 m/s

(a) Paverage=2π2mv A2f2

=2×(3.14)2×(6×103)×100×(103×2002)

=473×103=0.47 W

(b) Length of the string is 2m.

So, t=2100=0.02 sec

Energy =2π2mvf2A2t

=2×(3.14)2×6×(103)×100×2002×(103)2×(0.02)

=946.5×105

=9.46×103J=9.46 mJ


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