A wave is described by the equation `y = (1.0 mm) sin pi((x)/(2.0 cm) - (t)/(0.01 s))`.
(a) Find time period and wavelength.
(b) Find the speed of particle at `x = 1.0 cm` and time `t = 0.01 s`.
( c ) What are the speed of the partcle at `x = 3.0 cm`, `5.0 cm and 7.0 cm` at `t = 0.01 s`?
(d) What are the speeds of the partcle at `x =1.0 cm` at `t = 0.011` , `0.012 and 0.013 s`?

Answer

A, B, C, D

Explanation

(a) :. `T = (2pi)/(omega) = (2pi)/(pi//0.01) = 0.02 s`
`= 20ms`
`lambda = (2pi)/(k) =(2pi)/(pi//2)`
`= 4.0 cm`
(b) `v_(P) = (dely)/(delx)`
`= (-(pi)/(0.01)(mm)/(s)) cos pi((x)/(2.0 cm) -(t)/(0.01 s))`
`=( -(pi)/(10)(m)/(s)) cos pi((x)/(2.0 cm) -(t)/(0.01 s))`
Put `x= 1 cm` and `t = 0.01 s` in above equation
We get,
`v_(P) = 0`
( c ) and (d) Putting the given values in the above equation, we get the answer.