The equation of stationary wave along a stretched string is given by `y=5 sin ((pix)/(3)) cos 40 pi t `, where x and y are in cm and t in second. The separation between two adjacent nodes is

Options

A. 5 cm
B. 3 cm
C. 6 cm
D. 40 cm

Answer

B

Explanation

The given stationary wave produced on a string is represented by `y=5sin((pix)/(3))cos40pit" "...(i)`
The standard stationary wave produced on a string is represented by `y=2asinkxcosomegat" "...(ii)`
Comparing (i) and (ii), we get
`k=(pi)/(3)or(2pi)/(lambda)=(pi)/(3)orlambda=6cm`
The distance between two consecutive node is
`(lambda)/(2)=(6)/(2)cm=3cm`