C.3 · IB Physics
Wave superposition
Two travelling waves add point by point. Change each wave’s amplitude and wavelength, shift the phase, reverse wave 2, and watch the resultant: constructive, destructive, beats or a standing wave.
Predict first
Start from the default settings (equal waves, same direction, φ = 0°). Set the Phase difference φ to 180°. What is the resultant amplitude?
For equal waves A = √(A₁² + A₂² + 2A₁A₂cosφ). With φ = 180°, cosφ = −1, so A = |A₁ − A₂| = 0 and the waves cancel.
Check it in the model: Move the Phase difference φ slider from 0 to 180 and read the Resultant amplitude in the readout.
wave 1 wave 2 resultant
y₁ = A₁ sin(2πx/λ₁ − 2πvt/λ₁)
y₂ = A₂ sin(2πx/λ₂ ∓ 2πvt/λ₂ + φ)
v = 2.0 m s⁻¹ for both waves, f = v ÷ λ
same λ, same direction: A = √(A₁² + A₂² + 2A₁A₂cosφ)
Try this
- Use equal amplitudes and wavelengths and sweep the phase difference from 0° to 180°. At what φ does the resultant vanish, and what is the path difference then?
- Press the Beats preset. Read the frequency difference, then count how long the resultant takes to repeat its envelope.
- Choose Opposite direction with equal waves and find the nodes. How far apart are they compared with the wavelength?
Exam tip: Superposition means adding the displacements at each point, so two waves of equal amplitude and wavelength give twice the amplitude at zero path difference and zero at half a wavelength.