The displacement y (in cm) produced by a simple harmonic progressive wave is
`y = (10)/(pi) sin (2000pit- (pi x)/(15))`
What is the periodic time and maximum velocity of the particles in the medium ?

Options

A. `10^(-2)` sec and 2000 m/s
B. `10^(-3)` sec and 200 m/s
C. `10^(-3)` sec and 300 m/s
D. `10^(-4)` sec and 200 m/s

Answer

B

Explanation

`y = (10)/(pi) sin (2000 pi t - (pi x)/(15))`
Comparing this with the standard equation
`y = a sin (omega t - Kx)`, we get
`omega = 2000 pi and a = (10)/(pi) and K = (pi)/(15)`
`:. T = (2pi)/(omega) = (2pi)/(2000pi) = (1)/(1000) = 10^(-3)s`
and `v_("max") = a omega = (10)/(pi) xx 2000 pi`
`= 2000 xx 10 cm//s = 200 m//s`