Question

We know that waves transmit energy. There are many types of waves: light, microwaves, x-rays, sound waves, and ocean waves are all examples of waves transferring energy. Ocean waves are a renewable energy source that uses the energy of the waves to generate electricity.
Consider any ocean wave. What is the relationship between an ocean wave and the energy of that wave?
A. Wave energy decreases as the wave moves closer to shore.
B. The greater the wavelength, the more kinetic energy the wave has.
C. Wave energy increases with frequency and decreases with wavelength.
D. Wave energy is directly proportional to the amplitude of the wave.

Answer 1

Answer: D (with a correction).

The energy carried by an ocean surface wave depends mainly on its amplitude. In linear wave theory the average total energy per unit horizontal area is proportional to the square of the amplitude:
E = (1/2) ρ g a^2 (or equivalently E = (1/8) ρ g H^2, where H = 2a is wave height).

Why the other choices are incorrect:
- A: Not generally true — waves can shoal and increase in height near shore before breaking, and energy is dissipated mainly when waves break, so energy doesn't simply always decrease as they approach shore.
- B: Wavelength by itself does not determine the kinetic energy; for small-amplitude gravity waves the energy per unit area depends on amplitude squared, not on wavelength.
- C: That statement is true for photons (E = hf) but not for ocean gravity waves; energy does not generally increase with frequency (and decrease with wavelength) in the simple way implied.

So the closest answer is D, but strictly speaking energy is proportional to the square of the amplitude.