Question

Bob is studying waves in science and 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 1m, 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.

Answer 1

It's C

Step-by-step explanation:

Since E ∝ amplitude2 then as the amplitude is halved the energy is quartered.

Plugging in to check

amplitude2=E

22=4

12=1

Answer 2

For a simple harmonic motion energy is given with:

`E=(1)/(2)kA^2`
Where k is a constant that depends on the type of the wave you are looking at and A is amplitude.
Let's calculate the energy of the wave using two different amplitudes given in the problem:

`E_1=(1)/(2)k(1)^2=(1)/(2)k\\E_2=(1)/(2)k(2)^2=(4)/(2)k=2k\\`
We can see that energy associated with the wave is 4 times smaller when we decrease its amplitude by half. So the answer should be C.