(need to noww ). while bob is studying waves in science and he learns that the energy of a wave is directly proportional to the square of the waves amplitude. if the amplitude of a wave changes from 2m to 4m, what should he predict as the effect on energy of the wave? a) the energy is halved. b) the energy is doubled. c) the energy is quartered. d) the energy is quadrupled.

The energy is quadrupled. (D)

D) The energy is quadrupled.

Explanation:

Bobs found out from his study that energy of a wave is directly proportional to the square of the waves amplitude. This is expressed as:

E = kA² where:

E is the energy

A is the amplitude

k is the proportionality constant.

If the amplitude change from 2m to 4m, the initial amplitude is 2m and the final amplitude is 4m.

When A is 2m

E = k(2)²

E1 = 4K ... 1

As the amplitude increase to 4m, to energy becomes

E2 = k(4)²

E2 = 16k... 2

Taking the ratio of equation 2 to one to get the new energy E2 in terms of E1 will give:

E2/E1 = 16k/4k

E2/E1 = 4

E2 = 4E1

This shows that as the amplitude increases from 2m to 4m, the energy quadrupled