By what factor would the energy carried by the rope change

[looi76]

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

 

[Redbelly98]

First, by what factor does the amplitude change?

One consequence of the equation you wrote is that

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