Single Choice

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$$10$$
Correct Answer

Solution

$$y=5(sin4\pi t +\sqrt{3}cos4\pi t)$$
$$=5\times 2(\dfrac{1}{2}sin4\pi t+\dfrac{\sqrt{3}}{2}cos4\pi t)$$
$$=10(cos\dfrac{\pi}{3}sin4\pi t+sin\dfrac{\pi}{3}cos4\pi t)$$
$$=10sin(4\pi t+\dfrac{\pi}{3})$$
Hence the amplitude of the wave is $$10$$.

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