Question

# The energy of a sound wave is proportional to its amplitude squared. Why is it difficult to hear poolside sounds when swimming underwater?

Solution

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We would like to use our information about waves to explain why it is difficult to hear poolside sounds when swimming underwater.

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The sound wave will keep moving normally through the medium until it reaches another then part of the wave will transmit into the new medium and the other part will be reflected, and that depends on the density of the new medium.

In the case we are dealing with, the sound will travel in the air and at some point, it will hit the surface of the water, the water is denser than the air, so most of the wave will be reflected and part of the wave will be transmitted into the water with a small amplitude.

Because the energy of a sound wave is proportional to its amplitude, waves with small amplitudes have a small amount of energy, which explains why it is difficult to hear poolside sounds when swimming underwater where the transmitted waves have a very small energy.

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