Consider a sinusoidal travelling wave shown in figure. The wave velocity is `+ 40 cm//s`.
Find
(a) the frequency
(b) the phase difference between points `2.5 cm` apart
( c ) how long it takes for the phase at a given position to (pi//3)
(d) the velocity of a particle at `P` at the instant shown.

Options

A. `3pi//4 rad`
B. `5pi//4 rad`
C. `7pi//4 rad`
D. `9pi//4 rad`

Answer

b

Explanation

`lambda=2(4.5-2.5)=4 cm, v=nlambda`
`rArr n=(40)/(4)=10 Hz`
`phi=(2pi)/(lambda)Deltax=(5pi)/(4)rad implies phi=(2pi)/(T)Deltat`
`Deltat=(phi)/(2pin)=(pi//3)/(2pi10)=(1)/(60)s`
velocity of `p` should be maximum, as it is at mean position.
`v_(p)=omegaA=2pifA=2pixx10xx(2)/(100)`
`=1.26 m//s`
this velocity should be `-ve`, because slope at `p` is `+ve`.