Question

The wave function for a wave on a taut string isy(x, t) = 0.350 sin (10πt - 3πx + π/4)where x and y are in meters and t is in seconds. If the linear mass density of the string is 75.0 g/m .(a) what is the average rate at which energy is transmitted along the string?

Answer 1

The average rate at which energy is transmitted along the string is 15.1 J/s.

What is average power of a wave?

The average power of a sinusoidal wave is proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave

P  = ¹/₂μω²A²v

where;

• ω is angular frequency = 10π rad/s
• A is amplitude of the wave, = 0.35
• μ is linear mass density = 75 g/m = 0.075 kg/m
• k is angular wave number, k = 3π /m
• v is speed of the wave = ?

v = ω/k

v = (10π) / (3π)

v = 3.33 m/s

P = ¹/₂μω²A²v

P = ¹/₂(0.075)(10π)²(0.35)²(3.33)

P = 15.1 J/s

Thus, the average rate at which energy is transmitted along the string is 15.1 J/s.

Learn more about average power of a wave here: brainly.com/question/24228412

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