How does the average power of a wave depend on each of the following quantities?

Question

How does the average power of a wave depend on each of the following quantities?

A) The average power of a wave on a string is ________ the frequency
B) The average power of a wave on a string is ________ the tension of the string
C) The average power of a wave on a string is ________ the amplitude of the wave
D) The average power of a wave on a string is ________ the linear density of the string

Options include:

Proportional to the square of

proportional to the square root of

proportional to

inversely proportional to the square of

inversely proportional to the square root of

I have to fill in the blank for A, B, C, D

would also help to have some reasoning, if possible. I know that the average power formula is: P=.5*(mu)*v*(omega)^2*y^2m, just not sure how to proceed.

Explanation / Answer

here,

Power transmitted , P = 0.5 * u * w^2 * amplitude^2 * v = 0.5*u*w^2*A^2*lamda/T

u = mass per unit length

w = angular frequency

A = amplitude

T = tension

A)

The average power of a wave on a string is proportional to the square of the frequency

B)

The average power of a wave on a string is iversaly proportional to the tension of the string

C)

The average power of a wave on a string is proportionaltothe square of the amplitude of the wave

D)

The average power of a wave on a string is proportional to the linear density of the string

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