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
- A sound wave in air has frequency 440 Hz and speed 330 m/s. Find its wavelength.
- 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.
- Explain the difference between transverse and longitudinal waves with examples.
- A wave has a period of 0.02 s and wavelength 0.4 m. Calculate the wave speed.
- A slinky generates longitudinal waves with frequency 5 Hz and wavelength 0.3 m. Find the wave speed.