Question

Elaborate on the difference between the energy of the two waves seen here: Wave A has shorter waves but moves faster and Wave B has taller waves but moves slower.
A. Wave B has more energy: the amplitude of Wave B is double that of Wave A.
B. Wave energy is directly proportional to frequency and wavelength, therefore Wave A has more energy.
C. Wave A has more energy than Wave B because the wavelength of Wave A is greater.
D. Wave B has more energy than Wave A because the frequency of Wave B is greater.

Answer 1

Answer: A.

Explanation in brief:
- For a classical transverse wave (e.g. on a string) the average energy density is proportional to A^2 ω^2 (A = amplitude, ω = angular frequency) and the average power transmitted is P = (1/2) μ ω^2 A^2 v (μ = mass per unit length, v = wave speed). Thus amplitude enters as A^2 — doubling A gives four times the energy contribution from amplitude alone.
- Option A states Wave B’s amplitude is double Wave A’s; that by itself (all else equal) makes Wave B have more energy. The other options are incorrect: B is false (energy is not simply proportional to wavelength × frequency), C contradicts the given “shorter waves” description and is wrong, and D is wrong because nothing given supports Wave B having the higher frequency.

Note: if you need a definite numeric comparison you must also know the frequencies (or ω) and speeds; amplitude alone determines energy only when the other factors are held fixed. For electromagnetic radiation, energy per photon depends on frequency (E = hf), and amplitude controls intensity (number of photons), so the rules differ between mechanical and EM waves.