Question:
The phase velocity of a wave described by the equation $\Psi = \Psi_0 \, \sin (kx + \omega t + \pi / 2)$ is
The phase velocity of a wave described by the equation $\Psi = \Psi_0 \, \sin (kx + \omega t + \pi / 2)$ is
Updated On: Jun 7, 2024
- $\frac{x}{t}$
- $\frac{\Psi_0 } { \omega} $
- $\frac{\omega}{k}$
- $\frac{\pi} {2k}$
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The Correct Option is C
Solution and Explanation
Given,
$\psi=\psi_{0} \sin \left(k x+\omega t+\frac{\pi}{2}\right)$
Phase velocity of wave
$V=\frac{\omega}{k}=\frac{\text { Angular frequency }}{\text { Propagation constant }}$
$\psi=\psi_{0} \sin \left(k x+\omega t+\frac{\pi}{2}\right)$
Phase velocity of wave
$V=\frac{\omega}{k}=\frac{\text { Angular frequency }}{\text { Propagation constant }}$
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Concepts Used:
Wave Characteristics
The main properties of waves are as follows –
- Amplitude - The maximum displacement of the wave from the mean position is called the amplitude of the wave. It is the maximum height from the centre line to the crest or the trough. The crest is the highest point of the wave and the trough is the lowest point of the wave. Amplitude is measured in metres.
- Frequency - The number of vibrations passing a fixed point in a given amount of time is called frequency. The unit of frequency is Hertz.
- Wavelength - Wavelength is the distance between two identical points (adjacent crests or troughs). It is measured in metres. Frequency and wavelength are inversely proportional to each other.
- Time Period - The time taken by a complete wave to pass through a particular point is called the time period. The time period is measured in seconds. The time period is the reciprocal of the frequency.
- Speed - For a wave, speed is the distance travelled by a particular point on the wave in the given interval of time. Speed is measured in metres per second.