Motion of Waves
3.0 Properties of wave motion
3.1 General equation of wave motion
3.2 Wave function
3.3 Equation of a plane progressive harmonic wave
3.4 Important relations
3.0 Properties of wave motion
3.2 Wave function
3.3 Equation of a plane progressive harmonic wave
3.4 Important relations
- Amplitude: It is defined as the maximum displacement of a particle oscillating about its mean position. It is denoted by the symbol $A$.
- Wavelength: It is defined as the distance travelled by the wave during the time, the particle of the medium completes one oscillation about its mean position. It is also defined as the distance between two consecutive points in the same phase of the wave motion. It is denoted by symbol $\lambda $.
- In case of transverse wave, wavelength ($\lambda $) is the distance between two consecutive crests and troughs
- In case of longitudinal waves, wavelength ($\lambda $) is the distance between two consecutive compressions and rarefactions.
- Wave number: It is defined as the number of wavelength in the distance $2\pi$. It is denoted by the symbol $k$ It is also known as the propagation constant. Relation between wave number ($k$) and wavelength ($\lambda $) is given by, $$k = \frac{{2\pi }}{\lambda }$$
- Time period: It is defined as the time taken by a particle to complete one oscillation about its mean position. It is denoted by symbol $T$.
- Frequency: It is defined as the number of oscillations made by the particle in one second. It is denoted by symbol $f$. Relation between frequency ($f$) and time period ($T$) is given by, $$f = \frac{1}{T}$$
- Wave speed or speed of wave: It is defined as the distance travelled by the wave in one second. It is denoted by the symbol $v$. Mathematically, wave speed is given by, $$v = \lambda f$$ or $$v = \frac{\omega }{k}$$
Note: Speed of a wave depends on the properties of the medium. Although it is related to frequency and wavelength of a wave.
- Phase velocity: The velocity of the wave which maintains a constant phase for the wave is called phase velocity.
