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🌊 WAVES (Mechanical Waves)

Stage 3 – Page 5 : Doppler Effect (JEE Advanced)

1️⃣ What is Doppler Effect?

The Doppler Effect is the apparent change in frequency (or wavelength) of a wave due to relative motion between the source and the observer.

✔ Applies to sound waves, light waves, and water waves ✔ Most important for sound waves in JEE

2️⃣ General Doppler Formula (Sound Waves)

f′ = f × ( v ± v_o ) / ( v ∓ v_s )

v = speed of sound in medium
v_o = velocity of observer
v_s = velocity of source

⚠ Signs rule:
Observer towards source → + in numerator
Source towards observer → − in denominator

3️⃣ Special Cases

📌 (a) Moving Observer, Source at Rest

f′ = f ( v ± v_o ) / v

Observer approaching → frequency increases
Observer receding → frequency decreases

📌 (b) Moving Source, Observer at Rest

f′ = f × v / ( v ∓ v_s )

Source approaching → frequency increases
Source receding → frequency decreases

4️⃣ Wavelength Change Due to Moving Source

For a moving source:

λ_approach = ( v − v_s ) / f
λ_recede = ( v + v_s ) / f

✔ Frequency depends on observer
✔ Wavelength depends on source

5️⃣ Doppler Effect When Both Source & Observer Move

Always use general formula
Carefully choose signs
Relative motion matters, not absolute motion

6️⃣ Wind Effect (Very Important)

Wind changes speed of sound w.r.t. ground
Doppler frequency depends on motion relative to air
Wind alone does not cause Doppler shift

⚠ JEE Trap: Wind affects wavelength but NOT frequency heard

7️⃣ JEE Advanced Conceptual Traps

Using wrong sign convention
Confusing wind velocity with observer velocity
Assuming Doppler effect for standing waves
Ignoring medium (air) reference frame

8️⃣ Typical JEE Question Types

Police siren problems
Train–observer problems
Sound reflection with Doppler effect
Relative motion on circular paths

🎯 Final Takeaway

✔ Doppler effect = relative motion effect ✔ Signs decide everything ✔ Medium plays a key role

Stage 3 – Page 5 Completed Successfully ✅