Question

The maximum particle velocity is $3$ times the wave velocity of a progressive wave. If $A$ is the amplitude of oscillating particle, find phase difference between two particles of separation $x$.

Answer 1

The maximum particle velocity

$=3$ time wave velocity

$Aw=3v$

$\therefore w=\frac{3v}{A}$

As we know

$v=\lambda f$

$\therefore \lambda =\frac{v}{f}$

$or\lambda =\frac{v}{\frac{w}{2\pi }}=\frac{2\pi A}{w}=\frac{2\pi v}{\frac{3v}{A}}\therefore \lambda =\frac{2\pi A}{3}\varphi =phasedifference=\frac{2\pi }{\lambda }\times x=\left(\frac{2\pi }{\frac{2\pi A}{3}}\right)x=\frac{3x}{A}$