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

Answer

C

Explanation

A = 2 cm = 0.02 m, `upsilon` = 128 m/s
For five complete waves `5 lambda = 4 m rArr lambda = (4)/(5) m`
`y = A sin (Kx - omega t)`
`= A sin [(2pi x)/(lambda) - (2pi v)/(lambda) t]`
`= 0.02 si [(2pi xx 5)/(4) x - (2pi (128) xx 5)/(5)t]`
`= 0.02 sind [7.85 x - 1005.3 t]`