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

When the amplitude of the ocean wave increases by a factor of 1.1 ; The wave energy will increase by 1.21

The higher the amplitude of a wave the higher the energy produced by the wave therefore we can state that the energy produced by a mechanical wave is proportional to the square of its amplitude

Energy produced ∝ A²

∴ E = kA²

Given that the amplitude ( A )  increases by a factor of 1.1

E = k * ( 1.1 )²

where k is an unknown constant

E = ( 1.1 )² = 1.21

Hence we can conclude that the energy of the wave will increase by a factor of 1.21

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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

If A₂ = 1.1A₁, then

The energy increases by a factor of 1.2.