A transverse wave traveling along a string transports energy at a rate r . If we

Question

A transverse wave traveling along a string transports energy at a rate r. If we want to double this rate, we could

E) increase the amplitude of the wave by a factor of 8.

Please show how you got your answer.

A) increase the amplitude of the wave by a factor of 4. B) increase the amplitude by a factor of 8. C) increase the amplitude of the wave by a factor of 2. D) increase the amplitude by a factor of 2.

E) increase the amplitude of the wave by a factor of 8.

Please show how you got your answer.

Explanation / Answer

Mean power in a string P(t) = 2(pi) 2 A 2 u f 2 v

Where u = linear density of the string

            f = frequency

            v = velocity

           A = amplitude

i.e., power ot energy transport is directly proportional to square of the amplitude

     P ' / P = (A ' / A ) 2

Given P ' = 2P

2P / P = (A ' / A ) 2

    2 = (A ' / A ) 2

A ' / A = 2

      A ' = 2 A

So, answer is increase the amplitude by a factor of 2

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