Question

The equation of a travelling wave is $y=60cos(1800t-6x)$
where $y$ is in microns, $t$ in second and $x$ in metre. The ratio of maximum particle velocity to the velocity of wave propagation is

• A. $3.6\times {10}^{-4}$
• B. $3.6\times {10}^{-6}$
• C. $3.6\times {10}^{-8}$
• D. None of these

Answer 1

The correct option is A $3.6\times {10}^{-4}$

$y=60cos(1800t-6x),y$ is in microns.

$y=60cos(1800t-6x)\times {10}^{-6}$

$v=\frac{dy}{dt}$ = particle velocity$=60\times {10}^{-6}\times 1800sin(1800t-6x)$

$v_{particle,max}=6\times 18\times {10}^{-3}$

$v_{wave}=\frac{\omega }{k};\omega =1800;K=6$

$v_{wave}=\frac{1800}{6}=300$

$\frac{v_{particle.max}}{v_{wave}}=\frac{6\times 18\times {10}^{-3}}{300}$$=36\times {10}^{-5}=3.6\times {10}^{-4}$