sound

Chapter: Sound – Class 11 Notes

1. Introduction to Waves

A wave is a disturbance that transfers energy and momentum from one point to another without transfer of matter.

Types of Waves

• Mechanical Waves – Require material medium (sound, water waves)
• Electromagnetic Waves – Do not require medium (light)
• Matter Waves – Associated with moving particles

2. Common Properties of Waves

Amplitude (A): Maximum displacement from mean position.

Wavelength (λ): Distance between two consecutive particles in same phase.

Time Period (T): Time for one complete oscillation.

Frequency (n or f):

\[ n = \frac{1}{T} \]

Wave Velocity:

\[ v = \frac{\lambda}{T} \]

\[ v = n\lambda \]

Frequency remains constant when wave enters another medium. Speed and wavelength change.

3. Phase of a Wave

Phase describes the state of vibration of a particle.

• In phase – Same displacement and direction
• Out of phase – Different displacement or opposite motion
• Phase difference for one wavelength = \(2\pi\) radians

4. Transverse and Longitudinal Waves

Transverse Wave

• Particle vibration perpendicular to direction of propagation
• Has crests and troughs
• Can be polarised

Longitudinal Wave

• Particle vibration parallel to direction of propagation
• Has compressions and rarefactions
• Cannot be polarised
• Sound waves are longitudinal waves

5. Mathematical Expression of Progressive Wave

\[ y(x,t) = a \sin(kx - \omega t + \phi) \]

If wave moves in negative direction:

\[ y(x,t) = a \sin(kx + \omega t + \phi) \]

6. Speed of Sound

Newton’s Formula

\[ v = \sqrt{\frac{P}{\rho}} \]

Laplace Correction

\[ v = \sqrt{\frac{\gamma P}{\rho}} \]

For air, \( \gamma = 1.41 \)

7. Factors Affecting Speed of Sound

Temperature Effect

\[ v \propto \sqrt{T} \]

\[ v = v_0 + 0.61t \]

Speed increases by 0.61 m/s per 1°C rise.

Humidity Effect

Speed increases with increase in moisture.

8. Echo

Echo is repetition of sound due to reflection.

Minimum distance for echo ≈ 17 m.

9. Loudness

Intensity is proportional to square of amplitude:

\[ I \propto A^2 \]

Loudness in decibel:

\[ L = 10 \log \left(\frac{I}{I_0}\right) \]

Threshold intensity:

\[ I_0 = 10^{-12} \, W/m^2 \]

10. Doppler Effect

Apparent change in frequency due to relative motion.

\[ n = n_0 \frac{v \pm v_L}{v \mp v_S} \]

• Approach → Frequency increases
• Recede → Frequency decreases