Question

The equation of a travelling wave is y = 60 cos(1800 t - 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 x 10^-11
• B. 3.6 x 10^-6
• C. 3.6 x 10^-4
• D. 3.6

Answer 1

The correct option is C 3.6 x 10^-4

Maximum particle velocity $v_{max}=wa$ and wave velocity $v=\frac{w}{k}$
$\Rightarrow \frac{v_{max}}{v}=\frac{wa}{w/k}=ka.$ From the given equation k = Co-efficent of x=6 m
$a=60\times {10}^{-6}m$
$\Rightarrow \frac{v_{max}}{v}=ka=6\times {10}^{-6}\times 60=3.6\times {10}^{-4}$