Section 8.4: Wave Properties
Waves are disturbances that transfer energy without transferring matter. Key properties include wavelength, frequency, period, amplitude, and wave speed.
Wave speed: \[ v = f \lambda \]
where:
\( v \) = wave speed (m/s)
\( f \) = frequency (Hz)
\( \lambda \) = wavelength (m)
where:
\( v \) = wave speed (m/s)
\( f \) = frequency (Hz)
\( \lambda \) = wavelength (m)
Other important relations:
Period: \[ T = \frac{1}{f} \]
Angular frequency: \[ \omega = 2\pi f \]
Waves can be transverse (displacement perpendicular to direction of propagation) or longitudinal (displacement parallel to direction of propagation). Amplitude determines the wave's energy.
Example: Wave Speed Calculation
A wave on a string has a wavelength of 0.5 m and frequency 4 Hz. Find the wave speed.
\( v = f \lambda = 4 \times 0.5 = 2\,\text{m/s} \)
The wave speed is 2 m/s.
Practice Problems
- A wave with wavelength 1.2 m travels at 3 m/s. Find its frequency.
- A string vibrates with a frequency of 5 Hz and a wavelength of 0.8 m. Determine the wave speed.
- Explain the difference between transverse and longitudinal waves with examples.
- A sound wave travels 340 m/s and has a frequency of 170 Hz. Calculate its wavelength.
- A wave's amplitude is doubled. Explain the effect on its energy.