Q. A progressive wave in a medium is represented by the equation $y = 0.1\sin\left( 10\pi t - \frac{5}{11}\pi x \right)$ where y and x are in cm and t in second. The wavelength and velocity of the wave is
A) $\frac{5}{11}cm,\ 31.4\ cms^{- 1}$
B) $4.4cm,\ 22\ cms^{- 1}$
C) $2.2cm,\ 11\ cms^{- 1}$
D) $\frac{11}{5}cm,\ 22\ cms^{- 1}$
Explanation
(b) The progressive wave givesn is
$y = 0.1\sin\left( 10\pi t - \frac{5}{11}\pi x \right)$
Comparing it with general equation of progressive wave
Y=a sin (ωt-kx)
We get
$k = \frac{5\pi}{11}$
Or
$\frac{2\pi}{\lambda} = \frac{5\pi}{11}$
$\Longrightarrow \ \ \ \ \ \lambda = \frac{22}{5} = 4.4\ cm$
Moreover, ωt=10πt
Or 2πvt=10πt
$\therefore v = \frac{10\pi}{2\pi} = 5Hz\ $
$\therefore velocity\ v = \lambda v = 22\ cm\ s^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.