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 = (0.2) sin (7.85 x + 1005t)`
B. `y = (0.02) sin (15.7x - 2010t)`
C. `y = (0.02) sin (15.7x + 2010t)`
D. `y = (0.02) sin (7.85 x - 1005t)`

Answer

D

Explanation

Amplitude = 2 cm = 0.02m
There are 5 complete waves in 4 m
`:. 5 lamda = 4m :. lamda = (4)/(5) m = 0.8m`
The wave travels in the positive direction of the axis
`:.` The wave has the form of `y = A sin (Kx - omega t)` In this case,
`K = (2pi)/(lamda) = (2pi)/(0.8) = (2 xx 3.14 xx 10)/(8) = 7.85`
`v =(omega)/(K) :. 128 = (omega)/(7.85)`
`:. omega = 128 xx 7.85 = 1004`
`:.` The equation will be `y = 0.02 sin [7.85 x - 1005t]`