A small steel wire of diameter 1.0mm is connected to an oscillator and is under a tension of 5.7N . The frequency of the oscillator is 57.0Hz and it is observed that the amplitude of the wave on the steel wire is 0.54cm
What is the power output of the oscillator, assuming that the wave is not reflected back?
If the power output stays constant but the frequency is doubled, what is the amplitude of the wave?

a)

b) For this case we se that

Since the power is constant but the frequency is doubled we will see that

So the original amplitude is

And if the frequency is doubled we have that:

So then we will see that the amplitude would be reduced the half and for this case:

Explanation:

For this case we have the following data given:

represent the diameter

represent the radius

represent the tension

represent the frequency of the oscillator

represent the amplitude of the wave

Part a

For this case we can assume that the power transmitted to the wave is the same power of the oscillator. and we have the following formula for the power:

This expression can be written in different ways:

Where f is the frequency , T the tension the density of the steel, A the amplitude and the area, so then we have everuthing in order to replace and we got:

Part b

For this case we se that

Since the power is constant but the frequency is doubled we will see that

So the original amplitude is

And if the frequency is doubled we have that:

So then we will see that the amplitude would be reduced the half and for this case:

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