Question

Wave X has an amplitude of 2 meters. Wave Y has an amplitude of 6 meters. How does the energy of wave Y compare to the energy of wave X?

A.

It is nine times as great.

B.

It is three times as great.

C.

It is one-sixth as great.

D.

It is one-third as great.

Answer 1

The energy of wave Y is A.  It is nine times as great.

Explanation:

The energy of a wave is proportional to the square of the amplitude of the wave.

Mathematically:

$E\propto A^2$

where

E is the energy of the wave

A is its amplitude

In this problem, wave X has amplitude of 2 m, so

$A_x=2 m$

While wave Y has amplitude of 6 m, so

$A_y=6 m$

Therefore, the ratio of the energy of wave Y to that of wave X is

$\frac{E_Y}{E_X}=\frac{A_Y^2}{A_X^2}=\frac{6^2}{2^2}=\frac{36}{4}=9$

So, the energy of wave Y is nine times as great.

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Answer 2

Answer:

It is 9 times as great. : )

Explanation:

The energy carried by a wave is proportional to the square of the amplitude of the wave. Wave Y has an amplitude that is triple, or three times greater than, the amplitude of wave X. Therefore, the energy of wave Y is 32 = 9 times as great as the energy of wave X.