NEB Class 12 Physics Mechanical waves Notes in PDF Complete Handwritten. Physics Notes 2081: All Chapters | New Curriculum | Class 12 Physics Notes download.
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NEB Class 12 Physics Mechanical waves Note Handwritten in PDF
Speed of Wave Motion General Formula
For any mechanical wave: v = β(elastic property / inertial property)
- In solids: v = β(Y/Ο) where Y = Young’s modulus
- In liquids: v = β(B/Ο) where B = bulk modulus
- In gases: v = β(Ξ³P/Ο) (after Laplace correction)
Newton’s Formula And Why It Was Wrong
Newton assumed sound travels isothermally through air (temperature stays constant during compression and rarefaction).
Newton’s formula: v = β(P/Ο)
At STP (P = 1.013 Γ 10β΅ Pa, Ο_air = 1.293 kg/mΒ³): v = β(1.013 Γ 10β΅ / 1.293) β 280 m/s
But experimental value = 332 m/s. Huge discrepancy!
Why Newton was wrong: Sound propagation is extremely rapid β no time for heat exchange with surroundings. So the process is actually adiabatic, not isothermal.
Laplace’s Correction
Laplace recognized the process is adiabatic and replaced P with Ξ³P:
v = β(Ξ³P/Ο)
For air: Ξ³ = 1.4
v = β(1.4 Γ 1.013 Γ 10β΅ / 1.293) β 332 m/s β
This matches experiment. The derivation of Laplace’s correction is a guaranteed NEB exam question (short answer or long answer worth 2β4 marks).
Effect of Temperature on Speed of Sound
Using ideal gas law: P/Ο = RT/M (R = gas constant, M = molar mass)
So v = β(Ξ³RT/M), meaning v β βT (T in Kelvin)
- At 0Β°C (273 K): vβ β 332 m/s
- At temperature T K: v_T = vβ Γ β(T/273)
- For every 1Β°C rise, speed increases by approximately 0.61 m/s
- At 20Β°C: v β 344 m/s
NEB numerical type: “Sound travels at 332 m/s at 0Β°C. Find speed at 27Β°C.” Use: vβ/vβ = β(Tβ/Tβ) = β(300/273)
Effect of Pressure on Speed of Sound
At constant temperature, pressure has no effect on speed of sound.
Reason: Increasing pressure also increases density proportionally (from PV = nRT β P/Ο stays constant at constant T). So Ξ³P/Ο remains unchanged.
This is a commonly asked conceptual question: “Does increasing atmospheric pressure increase speed of sound?” Answer: No.
Effect of Humidity on Speed of Sound
Humid air is less dense than dry air at same temperature and pressure.
Reason: Water vapour (M = 18 g/mol) replaces heavier Nβ (28 g/mol) and Oβ (32 g/mol) molecules.
Since v β 1/βΟ β sound travels faster in humid air than dry air.
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Frequently Asked Questions
What is Laplace correction in Class 12 Physics?
Newton assumed sound travels isothermally giving v = β(P/Ο) β 280 m/s β far below experimental 332 m/s. Laplace corrected this: sound propagation is adiabatic not isothermal because it is too rapid for heat exchange. Corrected formula: v = β(Ξ³P/Ο). With Ξ³=1.4 for air this gives 332 m/s exactly.
What is Newton’s formula for speed of sound and its limitation?
Newton’s formula: v = β(P/Ο) assuming isothermal propagation gives approximately 280 m/s at STP. Experimental value is 332 m/s β a 16% error. The formula fails because sound propagation is actually adiabatic, not isothermal. Laplace corrected it by replacing P with Ξ³P giving the accurate result.
How does temperature affect speed of sound Class 12?
Speed of sound v = β(Ξ³RT/M), so v β βT where T is in Kelvin. For every 1Β°C rise in temperature, speed increases by approximately 0.61 m/s. At 0Β°C speed is 332 m/s. At 20Β°C speed is approximately 344 m/s. NEB numericals frequently ask you to find speed at a different temperature.
Does pressure affect speed of sound in Class 12 Physics?
At constant temperature, pressure has no effect on speed of sound. When pressure increases, density also increases proportionally (from PV = nRT). So the ratio P/Ο remains constant at constant temperature. Therefore Ξ³P/Ο stays unchanged and speed remains constant. This is a commonly asked conceptual question in NEB exams.
Why does sound travel faster in humid air than dry air?
Water vapour (molar mass 18 g/mol) is lighter than nitrogen (28 g/mol) and oxygen (32 g/mol) it replaces in humid air. Lower average molar mass means lower density. Since v = β(Ξ³P/Ο) and Ο decreases, speed increases. Humid air always has slightly higher sound speed than dry air at same temperature.
What is the speed of sound in solids and liquids Class 12?
Speed in solids: v = β(Y/Ο) where Y is Young’s modulus β approximately 5960 m/s in steel. Speed in liquids: v = β(B/Ο) where B is bulk modulus β approximately 1480 m/s in water. Both are much faster than in air (344 m/s) because elastic moduli of solids and liquids are much higher.
What is the formula for speed of sound in gas Class 12?
Speed of sound in gas after Laplace correction: v = β(Ξ³P/Ο) = β(Ξ³RT/M). Where Ξ³ = Cp/Cv ratio (1.4 for air), P is pressure, Ο is density, R is gas constant, T is temperature in Kelvin, M is molar mass. This is the fundamental formula for all speed of sound calculations in NEB Physics.
Which mechanical waves topics are most important for exam?
Most important: Laplace correction derivation and explanation (4 marks), Newton’s formula and its error (2 marks), effect of temperature on sound speed with formula (2 marks), effect of pressure and humidity conceptual questions (2 marks each). Laplace correction is asked in almost every NEB board paper.
