The displacement from the position of equilibrium of a point 4 cm from a source of sinusoidal oscillations is half the amplitude at the moment `t=T//6` (T is the time perios). Assume that the source was at mean position at `t=0`. The wavelength of the running wave is :

Options

A. 0.96 m
B. 0.48 m
C. 0.24 m
D. 0.12 m

Answer

B

Explanation

Equation of wave is `y=A sin (omegat-kx)`
`rArr A/2=A sin ((2pi)/TxxT/6-(2pi)/(lambda)xx4)`
`rArr (pi)/6=(pi)/3-(2pi)/(lambda)xx4rArr (2pi)/(lambda)xx4=(pi)/6`
`rArr lambda=48 cm`
`rArr lambda=0.48 meters`