Question

H/L increases toward 1/7 for a shoaling wave and eventually breaks, because as the

leading wave in the wave train slows: Hint: Look for how H and L change in a way
that will cause become steeper (i.e., H/L 1/7).
a. L decreases and PE is converted to KE.
b. No answer is correct – H/L can’t reach 1/7.
c. L decreases and KE is converted to PE
d. L increases and KE is converted to PE

Answer 1

As a wave shoals, its height increases and wavelength decreases because potential energy is converted to kinetic energy, leading to the critical steepness ratio of H/L = 1/7, at which the wave breaks.

Step-by-step explanation:

When a wave is shoaling, its height (H) increases and its wavelength (L) decreases as it approaches the shore. The ratio H/L becomes steeper and can reach the value of 1/7, at which point the wave is likely to break.

This occurs because as the leading wave in the wave train slows down due to the shallowing depth, potential energy (PE) is converted into kinetic energy (KE), resulting in a higher and narrower wave.

The decrease in L and the conversion of PE to KE are what cause the wave to steepen until it reaches the critical steepness and breaks.