Doppler Effect in Sound
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Direct answer
The Doppler effect is the change in apparent frequency due to relative motion of source and observer in a medium. The general formula is f' = f (v + v_o)/(v − v_s), with v the speed of sound, v_o positive when the observer moves toward the source and v_s positive when the source moves toward the observer. Any motion that closes the separation raises the pitch; motion that widens it lowers the pitch.
What you must remember
- Source toward a stationary observer: f' = f v/(v − v_s); away: f' = f v/(v + v_s). Observer toward a stationary source: f' = f (v + v_o)/v; away: f' = f (v − v_o)/v.
- The two cases are asymmetric: a moving source truly changes the wavelength in the medium, while a moving observer merely sweeps crests at a different rate — the same speed shifted between numerator and denominator gives different answers.
- A source passing an observer: the apparent frequency jumps downward from f v/(v − v_s) to f v/(v + v_s), never passing through f.
- Wind alters only the effective v: add the wind speed if it blows along the source–observer line from source to observer; crosswind components do nothing.
- No shift occurs for motion perpendicular to the line joining them (at closest approach), since the separation is momentarily unchanged.
- A moving reflector shifts the frequency twice — the wall acts as a moving observer and then a re-radiating moving source — doubling the effect.
- The formula assumes speeds well below v and motion along the line of sound.
Common confusion
The enduring error is putting speeds on the wrong side: the source speed belongs in the denominator, the observer speed in the numerator, and only components along the line of sound count. A reliable check: if the source moves, the wavelength in the air genuinely changes; if the observer moves, the wave pattern is untouched and only the crest-interception rate changes. Students also forget the medium — sound speeds are measured relative to air, so wind matters, unlike the relativistic Doppler effect for light where only relative motion enters.
Exam-focused takeaway
JEE Main tests the direct formula: a train's horn passing a platform, echo problems, a fork swung toward a listener — sign discipline is the whole battle. JEE Advanced extends to combined source and observer motion, wind along or across the line, and a source in circular motion (the shift falls from maximum through f at closest approach to minimum). Draw the source–observer line, mark which velocities close the gap, then substitute.
Frequently asked questions
Why do moving source and moving observer give different shifts?
A moving source crowds or spreads the wavefronts (the wavelength changes), while a moving observer leaves the wave pattern intact and merely intercepts crests at a different rate; the algebra preserves the difference.
How does wind enter the Doppler formula?
Only through the effective sound speed: v becomes v plus the wind speed when the wind blows from source toward observer along their line; a crosswind changes nothing.
What frequency is heard as a source passes?
It drops abruptly from f v/(v − v_s) to f v/(v + v_s), never passing through f.
Is there a shift during circular motion of the source?
Yes, except at closest approach: the line-of-sight velocity component varies continuously, so the heard frequency glides from maximum to minimum, passing through f when the motion is momentarily perpendicular.
Why is there no Doppler shift for perpendicular motion?
At that instant the source–observer distance is not changing, so no crests are gained or lost and the apparent frequency equals the emitted one.