The equation of a wave is given by
`y=10sin((2pi)/(45)t+alpha)`
If the displacement is 5 cm at t=0 ,then the total phase at t=7.5 sec is

Options

A. `(pi)/(3)`
B. `(pi)/(2)`
C. `(pi)/(6)`
D. `pi` .

Answer

B

Explanation

y = 10 sin `((2pi t)/(25) + a)`
at t = 0, y = 25 cm
`therefore ` 5 = 10 sin `(0 + alpha) rArr (1)/(2) = sin alpha`
`therefore alpha = 30^(@) or (pi)/(6)` radians.
Now at t = 7.5s. Total phase is
`phi = (2pi xx 7.5)/(45) + (pi)/(6) `
`phi = (pi)/(3) + (pi)/(6) = (pi)/(2) `
So correct choice is (b).