The equation of 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 :

Options

A. `3.6`
B. `3.6 xx 10^(-6)`
C. `(3.6 xx 10^(-11))`
D. `3.6 xx 10^(-4)`.

Answer

D

Explanation

y = 60 cos (1800 t - 6x )
comparing it with y = r cos `(omega t - kx)`
r = `60 xx 10^(-6) m " " omega = 1800 s^(-1) k = 6 m^(-1) `
v = `(omega)/(K) = (1800)/(6) = 300 ms^(-1)`.
now maximum particle velocity `V_(max).= r omega`
= 60 `xx 10^(-6) xx 1800 = 108 xx 10^(-3)`.
Now `(V_(max))/(v) = (108 xx 10^(-3))/(300) = 36 xx 10^(-5) = 3.6 xx 10^(-4)`
correct choice is (d).