Question

The equation of traveling wave is $y=30\cos (1800t-3x)$ where $y$ is in micro meter $t$ in sec and $x$ in meters. The ratio of the maximum particle velocity to velocity of wave propagation is

• A. $9\times {10}^{-5}$
• B. $2\times {10}^{-6}$
• C. $6\times {10}^{-6}$
• D. $1\times {10}^{-6}$

Answer 1

The correct option is B $2\times {10}^{-6}$

Given,

$y=30cos(1800t-3x)$

$K=3$

$\omega =1800$

Velocity of particle,

$v=\frac{\omega }{K}=\frac{1800}{3}$

$v=600m/s$

The wave propagate with the speed of light,

$c=3\times {10}^{8}m/s$

$\frac{v}{c}=\frac{600}{3\times {10}^8}$

$\frac{v}{c}=2\times {10}^{-6}$