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🌊 WAVES (Mechanical Waves)

Stage 3 – Page 10 : Doppler Effect & Advanced Applications (JEE Advanced)

                                               
Mechanical waves picture used in iit materials

1️⃣ Doppler Effect – Core Idea

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

✔ Occurs only due to relative motion
✔ Medium must be present (for sound)

2️⃣ General Doppler Formula (Sound Waves)

f' = f × (v ± vo) / (v ∓ vs)

  • v → Speed of sound in medium
  • vo → Velocity of observer
  • vs → Velocity of source

👉 Upper sign when moving towards
👉 Lower sign when moving away

3️⃣ Special Doppler Cases (JEE Favourite)

🔹 Only Observer Moving

f' = f (v + vo) / v

🔹 Only Source Moving

f' = f v / (v − vs)

🔹 Both Moving

f' = f (v + vo) / (v − vs)

4️⃣ Doppler Effect in Wind

  • Wind affects wavelength
  • Frequency depends only on relative motion
  • Doppler formula remains unchanged

⚠ Wind speed never adds directly to frequency

5️⃣ Apparent Frequency vs Actual Frequency

  • Frequency of source remains constant
  • Observer perceives changed frequency
  • Wavelength changes due to motion

✔ Medium determines wave speed, not frequency

6️⃣ Doppler Effect in Reflections

When sound reflects from a moving object:

  • Two Doppler shifts occur
  • One during reception
  • One during re-emission

👉 Extremely important for ambulance & radar-type problems

7️⃣ Shock Waves & Sonic Boom

  • Occurs when source speed > speed of sound
  • Wavefronts overlap
  • Creates a shock wave

Mach Number = vsource / vsound

✔ Mach > 1 → Supersonic motion

8️⃣ JEE Advanced Traps

  • Wrong sign usage in Doppler formula
  • Mixing wavelength change with frequency change
  • Ignoring double Doppler shift in reflection
  • Assuming Doppler exists without relative motion

9️⃣ One-Glance Formula Box

Doppler Effect:
f' = f (v ± vo) / (v ∓ vs)

Beat Frequency:
fbeat = |f₁ − f₂|

Resonance:
f = f₀

🔟 Final Waves Summary

✔ Superposition explains interference & beats
✔ Resonance gives maximum energy transfer
✔ Doppler effect depends on relative motion

🎯 WAVES – Stage 3 Completed Successfully 🎯
JEE Advanced Level Achieved ✅

📚 IIT–JEE Physics Complete Library (Class XI)

Curated for IIT-JEE Advanced Aspirants
Concepts • Numericals • Objective Questions • Revision Capsules

🔥 Kinetic Theory of Gases (KTG) – Complete Library

  1. KTG – Part 1
  2. KTG – Part 2
  3. KTG – Part 3
  4. KTG – Part 4
  5. KTG – Part 5
  6. KTG – Part 6
  7. KTG – Part 7
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  12. KTG – Part 12
  13. KTG – Part 13
  14. KTG – Part 14
  15. KTG – Part 15
  16. KTG – Part 16
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  18. KTG – Part 18
  19. KTG – Part 19
  20. KTG – Part 20
  21. KTG – Part 21
  22. KTG – Part 22
  23. KTG – Part 23
  24. KTG – Part 24
  25. KTG – Part 25
  26. KTG – Part 26
  27. KTG – Part 27
  28. KTG – Part 28
  29. KTG – Part 29
  30. KTG – Part 30

📐 Properties of Matter – Complete IIT-JEE Library

  1. Properties – Part 1
  2. Properties – Part 2
  3. Properties – Part 3
  4. Properties – Part 4
  5. Properties – Part 5
  6. Properties – Part 6
  7. Properties – Part 7
  8. Properties – Part 8
  9. Properties – Part 9
  10. Properties – Part 10
  11. Properties – Part 11
  12. Properties – Part 12
  13. Properties – Part 13
  14. Properties – Part 14
  15. Properties – Part 15
  16. Properties – Part 16
  17. Properties – Part 17
  18. Properties – Part 18
  19. Properties – Part 19
  20. Properties – Part 20
  21. Properties – Part 21
  22. Properties – Part 22
  23. Properties – Part 23
  24. Properties – Part 24
  25. Properties – Part 25

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