The wave described by y = 0.25 sin `(10 pi x - 2 pi t )` where x and y are in metres and t in seconds, is a wave travelling along the :

Options

A. `+` ve x -direction with frequency `pi` Hz and wavelength `lambda` = 0.2 m.
B. `+` ve x-direction with frequency 1 Hz and wavelength `lambda` = 0.2 m.
C. `-`ve x-direction with amplitude 0.25 m and wavelength `lambda` = 0.2 m
D. `-`ve x -direction with frequency 1 Hz.

Answer

B

Explanation

Given y = 0.25 sin `(10 pi x - 2pi t)`
y = 0.25 sin `(2 pi t - 10 pi x)`
We know that wave travelling along. + x -direction is
y = r sin `(omega t - kx)`
`therefore " " omega = 2pi and k = 10 pi `.
`rArr " " (2pi)/(lambda) = 10 pi " " therefore lambda = 0.2 ` m
Now `omega = 2pi ` f
`2 pi = 2 pi f " " rArr f = 1 ` Hz.