By what factor would the energy carried by the rope change

AI Thread Summary
The energy carried by a rope is proportional to the square of the amplitude of the wave. In this case, the initial amplitude is 15 mm and the new amplitude is 20 mm. The factor of change in amplitude is calculated as 20 mm / 15 mm, resulting in a factor of 1.33. Squaring this factor gives the change in energy, which is approximately 1.78. Therefore, the energy carried by the rope increases by a factor of 1.78 when the amplitude changes from 15 mm to 20 mm.
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Homework Statement


The amplitude of a wave in a rope is 15 \ mm. If the amplitude were changed to 20 \ mm. Keeping the frequency the same, by what factor would the energy carried by the rope change?

Homework Equations


intensity \propto (amplitude)^2

The Attempt at a Solution


amplitude_1 = 15 \times 10^{-3} \ m
amplitude_2 = 20 \times 10^{-3} \ m

What to do next:confused:
 
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First, by what factor does the amplitude change?

One consequence of the equation you wrote is that

\frac{I_2}{I_1} = (\frac{A_2}{A_1})^2
 
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