Question

during a rising tide, ocean waves often become larger. if the amplitude of a wave increases by a factor of 1.1, by how much does the energy increase?

Answer 1

Answer:

1.21 times

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, the amplitude of the wave increases by a factor of 1.1; it means that the new amplitude can be written as

$A'=1.1 A$

Therefore, this means that the energy of the wave increases by a factor:

$E'\propto A'^2=(1.1 A)^2 = 1.1^2 A^2 =1.21 A^2 = 1.21 E$

Therefore, the energy of the wave increases by a factor 1.21.