Question

A simple wave motion represented by $y=5(\sin 4\pi t+\sqrt{3}\cos 4\pi t)$. Its amplitude is:

• A. $5$
• B. $5\sqrt{3}$
• C. $10\sqrt{3}$
• D. $10$

Answer 1

Answer: (D)

$10$

$y=5(sin4\pi t+\sqrt{3}cos4\pi t)$

$=5\times 2(\frac{1}{2}sin4\pi t+\frac{\sqrt{3}}{2}cos4\pi t)$

$=10(cos\frac{\pi }{3}sin4\pi t+sin\frac{\pi }{3}cos4\pi t)$

$=10sin(4\pi t+\frac{\pi }{3})$

Hence the amplitude of the wave is $10$.