A stationary wave on a stretched string has an equation given by y = 10 sin `(2pi x)/(3)` cos 8 `pi`t, where x and y are in cm and t is in second. Then separation between the two adjacent nodes is given by :

Options

A. 1.5 cm
B. 3 cm
C. `(1)/(3) `cm
D. `(1)/(6) ` cm

Answer

A

Explanation

The general equation of stationary wave is
y = a sin kx cos `omega`t
y = 10 sin `(2pi x)/(3) ` cos 8`pi` t
so k = `(2pi)/(3) and omega = 8 pi `.
`(2pi)/(lambda) = (2pi)/(3) rArr lambda = 3` cm.
So distance between two consecutive nodes
` = (lambda)/(2) = 1.5` cm .
correct choice is a.