📚 Official Learning Libraries & Channels

🌊 Waves – JEE Advanced Objective Library

Complete Mechanical Waves objective questions from basic to toughest JEE Advanced level.

👉 Open Waves Library

📘 IIT-JEE Physics Master Library

Central hub covering all Physics chapters with structured IIT-level preparation.

👉 Open Physics Master Library

🏫 Learning Resource Hub

One-stop hub for all subjects, libraries, notes, and exam-oriented resources.

👉 Open Resource Hub

📢 WhatsApp Learning Channel

Daily updates, new libraries, exam tips, and instant notifications.

👉 Join WhatsApp Channel

🌊 WAVES (Mechanical Waves)

Stage 2 – Page 8 : Beats & Beat Frequency


1️⃣ What Are Beats?

Beats are produced when two sound waves of slightly different frequencies and nearly equal amplitudes interfere.

Result: Periodic increase and decrease in loudness of sound.


2️⃣ Necessary Conditions for Beats

  • Frequencies must be close (|f₁ − f₂| small)
  • Amplitudes must be nearly equal
  • Waves must travel in the same direction

3️⃣ Beat Frequency Formula

fbeat = | f₁ − f₂ |

This gives the number of beats heard per second.


4️⃣ Mathematical Explanation (JEE Favorite)

Superposition of two waves:

y = A sin(ω₁t) + A sin(ω₂t)

Resultant amplitude varies with time → beats are formed.


5️⃣ Time Period of Beats

Tbeat = 1 / |f₁ − f₂|

One complete loud–soft–loud cycle.


6️⃣ Maximum & Minimum Intensity

  • Maximum loudness: amplitudes add
  • Minimum loudness: amplitudes cancel

If amplitudes are unequal → sound never becomes zero.


7️⃣ Beats vs Interference

Beats Interference
Temporal variation Spatial variation
Frequency difference small Same frequency
Loud–soft sound Bright–dark pattern

8️⃣ Practical Applications

  • Tuning musical instruments
  • Finding unknown frequency
  • Detecting faulty tuning forks

9️⃣ JEE-Type Numerical

Two tuning forks produce 5 beats/sec. One fork has frequency 256 Hz. Find frequency of other fork.

Answer: 251 Hz or 261 Hz


🔟 Common JEE Traps

  • Large frequency difference → no beats
  • Unequal amplitudes → minimum loudness ≠ zero
  • Beats depend on frequency difference, not average frequency

➡️ Next Page Preview

  • Doppler Effect
  • Source & observer motion

Stage 2 – Page 8 Completed Successfully ✅

No comments:

Post a Comment

  📘 IIT–JEE Physics Complete Master Library (Class XI & XII) Concepts • Problems • Advanced Applications • Thinking Skill...