Q. The equation of a transverse wave travelling along positive x-axis with amplitude 0.2m, velocity $360\ ms^{- 1}$ and wavelength 60 m be written as
A) $y = 0.2\sin\pi\left\lbrack 6t + \frac{x}{60} \right\rbrack$
B) $y = 0.2\sin\pi\left\lbrack 6t - \frac{x}{60} \right\rbrack$
C) $y = 0.2\sin{2\pi}\left\lbrack 6t - \frac{x}{60} \right\rbrack$
D) $y = 0.2\sin{2\pi}\left\lbrack 6t + \frac{x}{60} \right\rbrack$
Explanation
(c) Given, a=0.2m
$v = 360\ ms^{- 1},\ \lambda = 60m$
Equations of transverse wave travelling along positive x-axis
$y = a\sin{2\pi\left\lbrack \frac{t}{T} - \frac{x}{\lambda} \right\rbrack}$
Or
$y = a\sin{2\pi\left\lbrack \frac{v}{\lambda}t - \frac{x}{\lambda} \right\rbrack}\ $
$y = 0.2\sin{2\pi\left\lbrack 6t - \frac{x}{60} \right\rbrack}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.