Speed of Sound

Sound is a mechanical wave, and its speed depends on the medium (air, water, solid) through which it travels.

General formula for wave speed:

\( v = \dfrac{d}{t} \)

\( v = f \lambda \)

Where:

• • \( v \) = speed of sound (m/s)
  • \( d \) = distance traveled (m)
  • \( t \) = time taken (s)
  • \( f \) = frequency (Hz)
  • \( \lambda \) = wavelength (m)

Factors affecting speed of sound

• Medium: Sound travels fastest in solids, slower in liquids, and slowest in gases because particle density and bonding affect vibration transfer.
• Temperature: In gases, speed increases with temperature because particles move faster.
  

  \( v \approx 331 + 0.6T \, \, \text{(m/s, with T in °C)} \)

• Pressure: At constant temperature, pressure has little effect since both pressure and density change proportionally.

Measurement of Speed of Sound

1. Echo Method

• • Clap or produce a loud sound near a large wall/cliff.
  • Measure time taken for the echo to return.
  • Total distance covered = \( 2d \) (to wall and back).

\( v = \dfrac{2d}{t} \)

2. Resonance Tube Method

• • A tuning fork of known frequency is struck and placed above a vertical resonance tube (partially filled with water).
  • When resonance occurs, sound becomes loudest → air column length \( L \) = \(\dfrac{\lambda}{4}\) (first resonance).
  • Speed is calculated as:

\( v = f \lambda \)

• • where \(\lambda = 4L\).

3. Time-of-Flight Method (modern)

• • Microphones and sensors are used to record the time taken for sound to travel a known distance.
  • This is more precise than echo method.