C.5 · IB Physics
Doppler effect
A moving source bunches its wavefronts ahead and stretches them behind, raising the frequency heard when approaching and lowering it when receding. The animation is in slow motion; the readouts use the real sound speed.
Predict first
Start from the defaults (source 135 m s⁻¹, f = 300 Hz, observer 0). Set Source speed to 270 m s⁻¹. The frequency heard ahead is about how many times f?
f′ = f v ÷ (v − vₛ) = f × 340 ÷ (340 − 270) = 4.86 f. The frequency rises steeply as vₛ approaches the wave speed.
Check it in the model: Move the Source speed, vₛ slider from 135 to 270 m s⁻¹ and read 'Heard by observer (ahead)' against the 300 Hz emitted.
source observer (arrow = its velocity)
f' = f (v − vₒ) ÷ (v − vₛ) (ahead)
f' = f (v + vₒ) ÷ (v + vₛ) (behind)
λ = (v ∓ vₛ) ÷ f
Try this
- Set the observer velocity to 0 and raise the source speed from 135 to 270 m s⁻¹. Compare the frequency heard ahead with the frequency heard behind.
- Press 'Observer runs away' (source 100 m s⁻¹, observer 140 m s⁻¹). Why is the frequency heard now barely different from f?
- Press 'Head-on' and check the heard frequency against f (v − vₒ) ÷ (v − vₛ) using vₒ = −140 m s⁻¹.
Common error: the wave speed in the medium does not change; for a moving source it is the wavelength that is compressed, and a moving observer changes the rate at which wavefronts are met, so the two cases must be handled separately.