Question

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

• A. $3.6\times {10}^{-11}$
• B. $3.6\times {10}^{-4}$
• C. $3.6\times {10}^{-9}$
• D. $3.6$

Answer 1

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

Velocity of wave propagation$=\frac{\omega }{k}$
$=\frac{1800}{6}$
$V=300m/sec$
$V_p=\frac{dy}{df}=-60\times 1800\sin (1800t-6x)\times {10}^{-6}$
$V_p=60\times 1800\times {10}^{-6}$
$\therefore \frac{V_p}{V}=\frac{60\times 1800\times {10}^{-6}}{300}$
$=3.6\times {10}^{-4}$