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Chapter 7: Mechanical Waves

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7.1 Speed of Wave Motion; Velocity of Sound in Solid & Liquid

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7.2 Velocity of Sound in Gas

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7.3 Laplaceโ€™s Correction

  • Observation: Experimental velocity of sound in air is slightly higher than P/ฯ\sqrt{P/\rho}P/ฯโ€‹ predicted by simple theory.
  • Reason: Air is not isothermal, but adiabatic โ†’ correction factor ฮณ.
  • Formula:
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ฮณ = 1/4 for air

7.4 Effect of Temperature, Pressure & Humidity

  • Temperature: v โˆ โˆšTโ€‹ย  โ†’ higher temperature, faster sound.
  • Pressure: For ideal gas at constant T, v independent of P.
  • Humidity: More water vapor โ†’ lower density โ†’ higher speed of sound.

Example: Air at 20ยฐC โ†’ v โ‰ˆ 343 m/s; at 30ยฐC โ†’ v โ‰ˆ 349 m/s

Important Questions and Answers in Short

Q1. What is Laplaceโ€™s correction?
๐Ÿ‘‰ Corrects sound velocity in gas from isothermal to adiabatic conditions.

Q2. Effect of temperature on sound velocity?
๐Ÿ‘‰ v โˆ โˆšT โ†’ higher temperature โ†’ faster sound.

Q3. Effect of pressure on sound velocity?
๐Ÿ‘‰ v independent of P for ideal gas at constant T.

Q4. Effect of humidity on sound velocity?
๐Ÿ‘‰ More humidity โ†’ faster sound.

โœ… Formula Sheet (Quick Revision)

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Numerical Examples

Example 1: Velocity of Sound in Solid

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Example 2: Effect of temperature on velocity of sound

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Example 3: Velocity of sound in Gas (air)

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