Question

If the amplitude of ocean waves increases by a factor of 1.1, by how much does the energy increase?

Answer 1

Answer:

The energy increases by a factor of 1.2.

Explanation:

The energy (E) of an ocean wave is directly proportional to the square of its amplitude (A).

E ∝ A² or E = kA²

If you have two waves with amplitudes A₁ and A₂, then

$\frac{E_{2} }{E_{1} } = \frac{A_{2}^{2} }{A_{1}^{2} } = (\frac{A_{2} }{A_{1} }})^{2}$

If A₂ = 1.1A₁, then

$E_{2} = E_{1} \times (\frac{1.1A_{1} }{A_{1} })^{2} = (1.1)^{2} = 1.2$

The energy increases by a factor of 1.2.