If two waves of the same frequency and amplit | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the equations of the two waves be $y_1 = a \sin(\omega t - kx)$ and $y_2 = a \sin(\omega t - kx + \phi)$.When they superpose,the resultant wav

Vedclass · Accepted Answer

$2\pi /3$

Vedclass · Answer

(D) Let the equations of the two waves be $y_1 = a \sin(\omega t - kx)$ and $y_2 = a \sin(\omega t - kx + \phi)$.When they superpose,the resultant wave is $y = y_1 + y_2$.Using the trigonometric identity $\sin A + \sin B = 2 \sin(\frac{A+B}{2}) \cos(\frac{A-B}{2})$,we get:$y = 2a \cos(\frac{\phi}{2}) \sin(\omega t - kx + \frac{\phi}{2})$.The resultant amplitude is $A_R = |2a \cos(\frac{\phi}{2})|$.Given that the resultant amplitude is equal to the individual amplitude $a$,we have:$a = |2a \cos(\frac{\phi}{2})| \implies \cos(\frac{\phi}{2}) = \pm \frac{1}{2}$.Considering the magnitude,$\cos(\frac{\phi}{2}) = \frac{1}{2}$.Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$,we have $\frac{\phi}{2} = \frac{\pi}{3}$.Therefore,the phase difference is $\phi = \frac{2\pi}{3}$.

If two waves of the same frequency and amplitude on superposition produce a resultant disturbance of the same amplitude,the waves differ in phase by

Similar Questions

There is a destructive interference between two waves of wavelength $\lambda$ coming from two different paths at a point. To get maximum sound or constructive interference at that point,the path of one wave is to be increased by

Two sound waves each of wavelength $\lambda$ and same amplitude $A$ interfere at point $Q$. If the path difference is $\frac{\lambda}{4}$, the amplitude of the resultant wave at point $Q$ is $[\sin \frac{\pi}{2} = 1, \cos \frac{\pi}{2} = 0]$

The resultant amplitude due to the superposition of two waves $y_1 = 5 \sin (\omega t - kx)$ and $y_2 = -5 \cos (\omega t - kx - 150^{\circ})$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module