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. 6 cm
B. 4 cm
C. 3 cm
D. `1.5` cm

Answer

c

Explanation

The standad equation of statonary wave is
`y=2 A sin kx. Cos omegat` …(i)
where, a is amplitude, `lambda` is wavelength.
Given, `y=5sin frac{pix}{3} cos 40 pit` ...(ii)
Comparing Eqs. (i) with (ii), we get
`k=pi/3 rArr (2pi)/lambda = pi/3 [because lambda=3 cm]` Distance between adjacent nodes `lambda/2=6/2=3` cm
`therefore lambda/2 = 3` cm