Doppler Effect in Sound (JEE Advanced)

“Doppler effect (in sound)”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: Wave motion, longitudinal and transverse waves, speed of the travelling wave.

JEE Main covers basic wave motion but does not include the Doppler Effect formula or its applications. For Advanced, you need to handle problems involving moving sources, moving observers, or both, often with reflections or multiple steps.

• The key idea: motion changes the effective wavelength between source and observer, which changes the frequency you hear.
• When source moves toward observer, wavelength gets compressed, so frequency increases. When source moves away, wavelength stretches, frequency decreases.
• When observer moves toward source, they encounter more wavefronts per second, so frequency increases. Moving away means fewer wavefronts, lower frequency.
• The speed of sound in the medium (v) stays constant. Only the relative positions of source and observer matter.
• For reflection problems (like sound bouncing off a wall or a moving car), treat the wall as a new source emitting the frequency it receives.
• Sign convention is crucial: always define positive direction clearly (usually from source to observer) and stick to it throughout the problem.

• Apparent frequency: f' = f × (v + v_o)/(v − v_s), where v = speed of sound, v_o = observer speed (+ if moving toward source), v_s = source speed (+ if moving toward observer)
• If source moves toward stationary observer: f' = f × v/(v − v_s)
• If observer moves toward stationary source: f' = f × (v + v_o)/v
• If both move toward each other: f' = f × (v + v_o)/(v − v_s)
• If both move away from each other: f' = f × (v − v_o)/(v + v_s)
• For reflection from a stationary surface: treat surface as observer first, then as source emitting received frequency
• Beat frequency when two frequencies are close: f_beat = |f_1 − f_2|
• No Doppler shift when motion is perpendicular to the line joining source and observer (for sound)

• Sign errors: forgetting that v_s is positive when source moves toward observer and negative when moving away. Always draw a diagram and define your positive direction first.
• Using the formula for light instead of sound. For sound, the medium matters and the formula is asymmetric in source and observer velocities.
• In reflection problems, forgetting that the process happens twice: first the wall receives a shifted frequency, then it acts as a source emitting that frequency to the original observer.
• Confusing frequency shift with intensity change. Doppler effect changes pitch (frequency), not loudness (intensity).

Question. A car moving at 36 km/h sounds a horn of frequency 500 Hz. The car approaches a large wall. A person sitting in the car hears the sound of the horn reflected from the wall. Find the beat frequency heard by the person. Speed of sound = 340 m/s.

Solved twice independently; both solutions agree.