Q. A simple wave motion represented by $y = 5\left( \sin{4\pi t + \sqrt{3}}\cos{4\pi t} \right)$. Its amplitude is
A) 5
B) 5$\sqrt{3}$
C) 10$\sqrt{3}$
D) 10
Explanation
(d) $y = 5\left( \sin{4\pi t + \sqrt{3}}\cos{4\pi t} \right)$
$y = 5\left( \sin{4\pi t + 5\sqrt{3}\cos{4\pi t}} \right)$
$A = \sqrt{A_{1}^{2} + A_{2}^{2}}$
$A = \sqrt{(5)^{2} + \left( 5\sqrt{3} \right)^{2}}$
$= \sqrt{25 + 75} = \sqrt{100}$
$A = 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.