Question 45: Waves

Question

When two progressive waves $${y_1} = 4\sin (2x - 6t)$$ and $${y_2} = 3\sin \left( {2x - 6t - {\pi  \over 2}} \right)$$ are superimposed, the amplitude of the resultant wave is __________.

Accepted Answer

Here, $${y_1} = 4\sin (2x - 6t)$$
$${y_2} = 3\sin \left( {2x - 6t - {\pi  \over 2}} ight)$$
The phase difference between two waves is $$\phi  = {\pi  \over 2}$$
The amplitude of the resultant wave is
$$A = \sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\cos \phi } $$
$$ = \sqrt {{4^2} + {3^2} + 2 	imes 4 	imes 3 	imes \cos {\pi  \over 2}}  = 5$$

Waves

When two progressive waves ${y_1} = 4\sin (2x - 6t) and {y_2} = 3\sin \left( {2x - 6t - {\pi \over 2}} \right)$ are superimposed, the amplitude of the resultant wave is __________.

Choose the correct answer: