Doppler EffectJEE Main

Concept

When a source and observer move relative to each other, the observed frequency changes — pitch rises as they approach and falls as they recede. This is why a passing siren drops in tone. The wave speed in the medium stays fixed; only the spacing of the wavefronts you meet changes.

Key formula

Derivation

An approaching source ($v_s>0$) emits each crest a little closer to the last, so the wavelength ahead shrinks to $(v - v_s)/f_0$ and the received frequency rises.

A moving observer ($v_o>0$) meets the crests faster, raising the rate by a factor $(v + v_o)/v$. Combining both effects gives $f' = f_0\,(v+v_o)/(v-v_s)$, with $v = 343\ \text{m/s}$ for sound in air.

Scenarios to explore

• Doppler Effect — How relative motion shifts the observed pitch.

Real-world applications

• Doppler radar and traffic speed guns.
• Medical ultrasound blood-flow measurement.
• Astronomical redshift of receding galaxies.

JEE exam tips

• Source in the denominator, observer in the numerator — memorise the structure.
• Both approaching: numerator up and denominator down, so the shift is largest.
• For light, use the relativistic formula instead — this one is for sound.

Common mistakes

• Swapping the sign convention — be consistent about which direction is positive.
• Putting the observer's speed in the denominator (it belongs in the numerator).
• Thinking the wave's speed changes — only frequency and wavelength shift, not $v$.

Exam traps to avoid

• If the source reaches the speed of sound a shock wave forms — the formula breaks down.
• Wind moving the medium changes $v$ for both terms, not just one.