Q. The equation of a simple harmonic wave is given by$y = 5\sin{\frac{\pi}{2}(100t - x)}$, where x and y are in metre and time is in second. The period of the wave in second will be
A) 0.04
B) 0.01
C) 1
D) 5
Explanation
(a) The given equation is
$y = 5\sin{\frac{\pi}{2}(100t - x)}\ \ \ldots(i)$
Comparing Eq. (i) with standard wave equation, given by
Y=a sin (ωt-kx) …(ii)
We have
$\omega = \frac{100\pi}{2} = 50\pi$
$\Longrightarrow \ \frac{2\pi}{T} = 50\pi$
$\Longrightarrow T = \frac{2\pi}{50\pi} = 0.04\ s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.