A wave in a string has an amplitude of `2 cm`. The wave travels in the `+ve` direction of x axis with a speed of 1`28 ms^-1` and it is noted that `5` complete waves fit in `4 m` length of the string. The equation describing the wave is

Options

A. `y=(0.02) m sin (15.7x-2010t)`
B. `y=(0.02) m sin (15.7x+2010t)`
C. `y=(0.02) m sin (7.85x-1005t)`
D. `y=(0.02) m sin (7.85x+1005t)`

Answer

C

Explanation

Here, amplitude `r=2cm =0.02m, upsilon=128m//s`
`lambda=(4)/(5)=0.8m, v=(upsilon)/(lambda)=(128)/(0.08)=160Hz,`
`omega=2piv=2xx(22)/(7)xx160=1005`
and `k=(2pi)/(lambda)=(2xx(22//7))/(0.8)=7.85`
Now `y=rsin (kx-omegat)`
`=0.02 sin (7.85x-1005t)`