Section 3.7: Mechanical Waves Review

Mechanical waves transfer energy through a medium without transporting matter. This section reviews the key properties and types of mechanical waves, including transverse and longitudinal waves.

Wave Properties:
  • Wave speed: \( v = f \lambda \)
  • Amplitude: Maximum displacement from equilibrium
  • Frequency: Number of oscillations per second
  • Period: Time for one oscillation, \( T = 1/f \)
  • Wavelength: Distance between two consecutive points in phase
  • Energy transport depends on amplitude and frequency

Example 1

A wave has a wavelength of 0.5 m and frequency 2 Hz. Find the wave speed.

Wave speed: \( v = f \lambda = 2 \times 0.5 = 1 \text{ m/s} \)

Example 2

A string vibrates with frequency 50 Hz and wave speed 100 m/s. Find the wavelength.

Wavelength: \( \lambda = v / f = 100 / 50 = 2 \text{ m} \)

Practice Problems

  1. A sound wave in air has frequency 440 Hz and speed 330 m/s. Find its wavelength.
  2. A transverse wave on a string has amplitude 0.05 m and wavelength 1 m. If the wave speed is 2 m/s, find the frequency.
  3. Explain the difference between transverse and longitudinal waves with examples.
  4. A wave has a period of 0.02 s and wavelength 0.4 m. Calculate the wave speed.
  5. A slinky generates longitudinal waves with frequency 5 Hz and wavelength 0.3 m. Find the wave speed.