a waves amplitude is 0.5 meters. If the amplitude is increased to 1 metro, how does its energy change

The energy becomes 4 times greater.

Explanation:

We know that the energy of a wave is proportional to the square of its amplitude

E ∝ Amplitude^2

Since the original amplitude = 0.5 m

and the new amplitude becomes = 1 m

We are doubling the amplitude. This means that the new energy will be affected by a factor of 4

E_new ∝ (2*Amplitude) ^2 =

E_new ∝ 4 * (Amplitude) ^2

E_new = 4*E