Doppler Lab

Class XI · Waves: Doppler effect with moving source & observer.

Controls

Source velocity vₛ60 m/s

Observer velocity v₀0 m/s

Source frequency fₛ2.0 Hz

Sound speed v120 m/s

Live readouts

fₛ (emitted)2.00 Hz

f_obs4.00 Hz

Shift+2.00 Hz

v_s toward observer60 m/s

v_o toward source0 m/s

Formula

Doppler effect (1-D):
  f_obs = fₛ · (v ± v₀) / (v ∓ vₛ)

Sign helper (toward = positive):
  v₀ : + if observer moves toward source
  vₛ : + if source moves toward observer

Then:
  f_obs = fₛ · (v + v₀)/(v − vₛ)

If vₛ ≥ v ⇒ supersonic ⇒ shock cone.

Try this: Set vₛ = +120, v₀ = 0: wavefronts pile up ahead of the source: observer (to the right) hears higher f. Now set vₛ = −120: the same observer hears lower f (red-shifted). Push vₛ → vSound: f_obs blows up: that's the sonic boom limit.

Doppler Lab

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