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A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m-1 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.

A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m-1 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.

Grade:11

1 Answers

Jitender Pal
askIITians Faculty 365 Points
7 years ago
Sol. . A = 1 mm = 10–3 m, m = 6 g/m = 6 * 10–3 kg/m T = 60 N, f = 200 Hz ∴ V = √T /m = 100 m/s a) Paverage = 2π2 mv A2f2 = 0.47 W b) Length of the string is 2 m. So, t = 2/100 = 0.02 sec. Energy = 2π2 mvf2A2t = 9.46 mJ.

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