The equation of a wave motion is given by `y = 7 sin(7pi t - 0.4 pi x + (pi)/(3))`, where all quantities are measured in SI units. Then the ratio of wave velocity to the maximum particle velocity is

Options

A. `5 : 44`
B. `44 : 5`
C. `22 : 7`
D. `22 : 5`

Answer

A

Explanation

`y = 7 sin (7pi t- 0.4 pi x + (pi)/(3))`
`omega = 7pi and k = 0.4 pi `
`(v)/(v_(P)) = (n lamda)/(A omega) = (n lamda)/(4 xx 2pi n) = (1)/(A xx (2pi)/(lamda))`
`= (1)/(Ak) = (1)/(7 xx 0.4 pi) = (1)/(7 xx 0.4) xx (22)/(7)`
`= (10)/(4 xx 22) = (5)/(44)`