Question

A student creates two waves (one green and one red) and plots them on the same graph.
A graph with two waves. One wave has a greater amplitude than the other. Wave length is similar with both waves.

Answer 1

Do you want an explanation of what the plot shows, a comparison of the two waves, or what happens when the two are combined? A few useful points depending on what you mean:

- How to read the plot
- Amplitude: the green wave (the taller peaks) has the larger amplitude. Amplitude is the maximum displacement from the central axis.
- Wavelength: since the distance between peaks is the same for both traces, they have the same wavelength (and therefore the same frequency, if plotted versus time).

- If these are mechanical waves (e.g., on a string)
- Energy and intensity of a wave scale like amplitude squared, so the larger-amplitude (green) wave carries more energy/intensity: E ∝ A^2.

- If these are electromagnetic waves (light)
- In classical terms intensity ∝ amplitude^2, so larger amplitude → higher intensity.
- But photon energy depends on frequency (E = hf). If the wavelengths really are the same, the green and red traces cannot represent real red and green light simultaneously (red and green light have different wavelengths/frequencies). If the traces are just colored for clarity, then equal wavelength → equal photon energy; a larger amplitude then just means higher intensity, not higher photon energy.

- If you superpose the two waves (same wavelength/frequency)
- Let y1 = A1 sin(θ + φ1), y2 = A2 sin(θ + φ2) where θ = kx − ωt. Their sum has resultant amplitude
Ares = sqrt(A1^2 + A2^2 + 2 A1 A2 cos(Δφ)),
where Δφ = φ2 − φ1.
- Special cases: in phase (Δφ = 0) → Ares = A1 + A2 (maximum constructive interference); out of phase (Δφ = π) → Ares = |A1 − A2| (partial or full cancellation).

If you want, tell me whether these are light or mechanical waves and whether you want the algebraic sum or a plot; I can compute or draw the resultant wave for given amplitudes and phase difference.