A transverse wave travelling on a taut string is represented by:
`Y=0.01 sin 2 pi(10t-x)`
Y and x are in meters and t in seconds. Then,

Options

A. The speed of the wave is `10m//s`.
B. closet points on the string which differ in phase by `60^(@)` are `(1//6)m` apart
C. maximum particle velocity is `pi//4 m//s`
D. the phase of a certain point on the string changes by `120^(@)` in `(1//20)` seconds.

Answer

a., b.

Explanation

`y=0.01 sin [2pi(10t-x)]`
`impliesy=0.01sin[20pit-2pix]`
`omega=20pi, K=2pi`
Wave velocity :`v=(omega)/(k)=(20pi)/(2pi)=10m//s`
`Deltaphi=K Deltax`, given `Deltaphi=60^(@)=(pi)/(3)`
`(pi)/(3)=2pi DeltaximpliesDeltax=(1)/(6)m`
`v_(p-max)=omegaA=20pixx0.01=(pi)/(5)m//s`
`Deltaphi_(t)omegaDeltat=20pixx(1)/(20)=pi`
so in time `(1)/(20)s`, phase changes by and not `120^(@)`