Question

Explain what is plane progressive harmonic wave?

Answer 1

Step 1: Definition of plane progressive harmonic wave

1. A plane progressive wave is a wave that travels uniformly in a particular direction.
2. A simple harmonic motion occurs when the restoring force acting on an oscillating particle is directly proportional to the displacement of the object. This restoring force acts towards the equilibrium position of the particle.
3. Hence, a plane progressive wave is a wave that travels uniformly in a particular direction such that each particle in the wave undergoes a simple harmonic motion about their mean positions with uniform amplitude and wavelength.

Step 2: Diagram of plane progressive harmonic wave

Step 3: Equation of plane progressive harmonic wave,

The displacement of a particle from equilibrium position at time $t$ is given by
$y=asin(\omega t-\phi )$
where, $a$=amplitude, $\omega =$Angular Frequency and $\phi =$phase difference
Phase difference depends on the path difference $OP$
$\phi ={\displaystyle \frac{2\pi x}{\lambda }}$
where, $x=$path difference and $\lambda =$ wavelength.
$y=a\sin (\omega t-{\displaystyle \frac{2\pi x}{\lambda }})$
$\therefore y=a\sin (\omega t-kx)$ $\left[\because k=\frac{\text{2}\pi }{\lambda }\right]$
Where, $k$ is a wave number.