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👉 Join WhatsApp Channel🌊 WAVES (Mechanical Waves)
Stage 1 – Page 4 : Speed of Mechanical Waves
1️⃣ What Determines Wave Speed?
Very important concept: Wave speed depends only on the properties of the medium, not on amplitude or frequency.
JEE Rule:
Changing frequency changes wavelength, not speed.
2️⃣ Speed of Transverse Waves on a Stretched String
For a stretched string:
v = √(T / μ)
| Symbol | Meaning |
|---|---|
| T | Tension in the string |
| μ | Mass per unit length (kg/m) |
Key observations:
- More tension → wave travels faster
- Heavier string → wave travels slower
3️⃣ Effect of Changing Parameters (String)
- If tension becomes 4T → speed becomes 2v
- If μ becomes 4μ → speed becomes v/2
IIT Shortcut:
v ∝ √T and v ∝ 1/√μ
4️⃣ Speed of Longitudinal Waves (Sound Waves)
Speed of sound depends on elasticity and density:
v = √(Elastic Modulus / Density)
5️⃣ Speed of Sound in Different Media
🔹 In Solids
v = √(Y / ρ)
🔹 In Liquids
v = √(B / ρ)
🔹 In Gases
v = √(γP / ρ)
| Symbol | Meaning |
|---|---|
| Y | Young’s modulus |
| B | Bulk modulus |
| γ | Ratio of specific heats |
| ρ | Density |
6️⃣ Order of Speed of Sound
- Fastest → Solids
- Medium → Liquids
- Slowest → Gases
Reason:
Higher elasticity and closely packed particles.
7️⃣ Speed of Sound in Air (Important Values)
- At 0°C → 331 m/s
- At 20°C → ~343 m/s
Approximate formula:
v = 331 + 0.6T (T in °C)
8️⃣ Factors Affecting Speed of Sound in Air
- Temperature → increases speed
- Humidity → increases speed
- Pressure → no effect (at constant temperature)
9️⃣ Common JEE Mistakes
- Thinking louder sound travels faster ❌
- Thinking frequency changes speed ❌
- Ignoring medium properties ❌
🧠 Exam Thinking Method
- First identify type of wave
- Choose correct speed formula
- Relate speed with λ and f if needed
Stage 1 – Page 4 Completed ✅
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