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👉 Join WhatsApp Channel🌊 WAVES (Mechanical Waves)
Stage 1 – Page 5 : Energy, Power & Intensity of Waves
1️⃣ Energy Transport in Waves
A mechanical wave does not transport matter, but it transports energy through the medium.
JEE Concept:
Particles oscillate about their mean position, but energy travels forward.
2️⃣ Energy in a Transverse Wave on a String
For a stretched string, total energy of a wave depends on:
- Amplitude (A)
- Frequency (f)
- Mass per unit length (μ)
- Wave speed (v)
Total Energy ∝ A²
3️⃣ Kinetic Energy vs Potential Energy
In a transverse wave on a string:
- Average Kinetic Energy = Average Potential Energy
- Energy keeps converting between KE and PE
IIT Insight:
At mean position → KE maximum, PE minimum
At extreme position → PE maximum, KE zero
4️⃣ Power Transmitted by a Wave
Power = Energy transmitted per unit time
P = ½ μ ω² A² v
| Symbol | Meaning |
|---|---|
| μ | Mass per unit length |
| ω | Angular frequency (2πf) |
| A | Amplitude |
| v | Wave speed |
5️⃣ Key Power Relationships (Must Remember)
- P ∝ A² → doubling amplitude increases power 4 times
- P ∝ f² → higher frequency carries more power
- P ∝ v → faster wave transmits more power
6️⃣ Intensity of a Wave
Intensity is power transmitted per unit area:
I = P / A
SI unit: W/m²
7️⃣ Intensity of Sound Waves
For sound waves:
I ∝ A²
- Louder sound → higher intensity
- Amplitude decides loudness
8️⃣ Sound Level (Decibel Scale)
Sound intensity level is measured using:
β = 10 log₁₀ (I / I₀)
Where:
- I₀ = 10⁻¹² W/m² (threshold of hearing)
- Unit: decibel (dB)
9️⃣ Typical Sound Levels
| Sound | Level (dB) |
|---|---|
| Whisper | 20–30 |
| Normal conversation | 60 |
| Traffic | 80–90 |
| Pain threshold | 120 |
🔟 Common JEE Traps
- Loudness ≠ Intensity (subjective vs objective)
- Amplitude affects energy, not speed
- Decibel scale is logarithmic, not linear
🧠 JEE Problem-Solving Tip
- Check proportionality first
- Square relationships are very common
- Use ratios instead of absolute values
Stage 1 – Page 5 Completed ✅
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