The equations of displacements of two waves are given as $y_1 = 10 \sin \left(3\pi t + \frac{\pi}{3}\right)$…
The equations of displacements of two waves are given as $y_1 = 10 \sin \left(3\pi t + \frac{\pi}{3}\right)$, $y_2 = 5 (\sin 5\pi t + \sqrt{3} \cos 5\pi t)$. Then, what is the ratio of their amplitudes?
1 : 2
2 : 1
1 : 1
None of these
Solution
Given, $y_2 = 5(\sin 5\pi t + \sqrt{3}\cos 5\pi t)$
[A vector triangle diagram shows horizontal component 5, vertical component $5\sqrt{3}$, hypotenuse 10, and phase angle $\phi$.]
This can also be written as $y_2 = 10 \sin\left(5\pi t + \frac{\pi}{3}\right)$
Now, $A_1 = 10$ and $A_2 = 10$
$\therefore \frac{A_1}{A_2} = \frac{1}{1}$