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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 ✅
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