Question

Elaborate on the difference between the energy of the two waves seen here:



(1 point)
Responses

Wave energy is directly proportional to frequency and wavelength, therefore Wave A has more energy.
Wave energy is directly proportional to frequency and wavelength, therefore Wave A has more energy.

Wave B has more energy than Wave A because the frequency of Wave B is greater.
Wave B has more energy than Wave A because the frequency of Wave B is greater.

Wave B has more energy: the amplitude of Wave B is double that of Wave A.
Wave B has more energy: the amplitude of Wave B is double that of Wave A.

Wave A has more energy than Wave B because the wavelength of Wave A is greater.

Answer 1

You need to know which wave property actually controls energy. For most macroscopic (mechanical or classical EM) waves the energy transported (or intensity) is proportional to the square of the amplitude. For a mechanical wave on a string the average energy per unit length ∝ A^2 ω^2 (so it depends on amplitude squared and on frequency squared through ω = 2πf). For a classical EM wave the energy density (and intensity) ∝ E-field amplitude^2. For a single photon (quantum EM) the energy of each photon is proportional to frequency, E = hf.

So:
- If the two pictured waves differ in amplitude, the one with larger amplitude carries more energy (and doubling the amplitude gives four times the energy/intensity).
- If they differ only in frequency and you are talking about photons, higher frequency means higher photon energy; for classical waves higher frequency also increases energy (via ω^2 for mechanical waves).
- The statement “energy is directly proportional to frequency and wavelength” is wrong (wavelength and frequency are inversely related for a given wave speed).

If the picture shows Wave B with twice the amplitude of Wave A (and amplitudes are the only difference), the correct choice is: “Wave B has more energy: the amplitude of Wave B is double that of Wave A.”