The wave function for a wave on a taut string is where x and y are in meters and

Question

The wave function for a wave on a taut string is

where x and y are in meters and t is in seconds. The linear mass density of the string is 93.5 g/m.

(a) What is the average rate at which energy is transmitted along the string?

(b) What is the energy contained in each cycle of the wave?

The wave function for a wave on a taut string is where x and y are in meters and t is in seconds. The linear mass density of the string is 93.5 g/m. What is the average rate at which energy is transmitted along the string? What is the energy contained in each cycle of the wave?

Explanation / Answer

v = w/k = 9pi/3pi = 3

a)

rate or avg. power , P = (1/2)mu * w^2 * A^2 v

= (1/2)*(93.5*10^-3)*(9*pi)^2*(0.325)^2*3

= 11.8428 W

b)

E = P*T = 11.8428*(2*pi/(9*pi)) = 2.631733 J

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