Question

which graph shows how energy and the amplitude of waves are related?

Explanation:

Step1: Recall the relationship between wave energy and amplitude

The energy \(E\) of a wave is proportional to the square of its amplitude \(A\), i.e., \(E\propto A^{2}\).

Step2: Analyze the first graph

The first graph is a straight - line graph (linear relationship \(y = mx\)). If \(E\) were proportional to \(A\) ( \(E=kA\) where \(k\) is a constant), this would be the case. But since \(E\propto A^{2}\), this is not the correct relationship.

Step3: Analyze the second graph

The second graph is a curve. For a function \(y = kx^{2}\) (a quadratic function), when \(x = 1,y=k\); when \(x = 2,y = 4k\); when \(x=3,y = 9k\) etc. This matches the \(E\propto A^{2}\) relationship.

Answer:

The second graph (the one with a curved line, showing a non - linear, quadratic - like relationship) shows how energy and the amplitude of waves are related.