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 meter 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) $y = 5\ \sin{\frac{\pi}{2}(100t - x)}$
$y = 5\ \sin\left( \frac{100\pi}{2}t - \frac{\pi}{2}x \right)$
$y = 5\ \sin\left( 50\pi t - \frac{\pi}{2}x \right)$
The general equation
$y = a\sin(\omega t - kx)$
$\therefore\omega = 50\pi$
$T = \frac{2\pi}{\omega} = \frac{2\pi}{50\pi} = \frac{1}{25}$
Or $T = 0.04\ s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.