Question

A wave on a small lake has an amplitude of 0.1. What happens to the energy of the wave by doubling its height to 0.2 meters

Answer 1

As we know that energy of wave depends on amplitude as per following relation

$E = kA^2$

here we know that

k = constant

A = amplitude of wave

here we know that amplitude is doubled

so here as per above formula the energy of wave will increase by 4 times

as we know that

$E = k(2A)^2$

so energy is 4 times of initial value