A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x=0. it begins with a displacement y=0, at t=0, according to equation `y=0.2 sin (kx+-omegat)`. How much time passed between the first two instant when this particle has a displacement of y=0.1 m?

Options

A. 1.9 ms
B. 3.9 ms
C. 2.4 ms
D. 0.5 ms

Answer

a

Explanation

`y=(0.2 m) sin [kx+-omegat]`
for `x=0, y=0.1 m`
`0.1=0.2 sin(omegat)`
`impliesomegat=pi//6 or 5pi//6`
So, `t_(2)=5pi//6omega` and `T_(1)=pi//6omega`
`t_(2)-t_(1)=2pi//3omega=1//3f=1.9 ms`