3.2 Description of Waves
Wave Characteristics:
- **Wavelength (λ):** The distance between
two consecutive points that are in phase on a wave, such as crest to crest or
trough to trough in a transverse wave, or compression to compression in a
longitudinal wave.
- **Amplitude (A):** The maximum displacement of a particle from its
equilibrium position. Amplitude is related to the energy of the wave; higher
amplitude means more energy.
- **Frequency (f):** The number of complete oscillations or cycles that occur
per unit time, typically measured in Hertz (Hz).
- **Period (T):** The time taken for one complete cycle of the wave. It is the
reciprocal of frequency, T = 1/f.
- **Wave Speed (v):** The speed at which the wave propagates through the
medium, given by the relationship:
v = fλ
Wave Equation:
The general equation for a wave traveling
along a medium can be expressed as:
y(x,t) = A sin(kx - ωt + φ)
where:
- y(x,t) is the displacement at position x and time t,
- A is the amplitude,
- k is the wave number (k = 2π/λ),
- ω is the angular frequency (ω = 2πf),
- φ is the phase constant.
Example Problem:
A wave on a string has a frequency of 5 Hz
and a wavelength of 2 meters. What is the speed of the wave?
Solution:
Using the wave speed formula:
v = fλ = 5 Hz × 2 m = 10 m/s
The speed of the wave is 10 meters per second. | 
