Equations of motion for two waves traveling i | vedclass

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

Question

(C) The given wave equations are $y_1 = A_1 \sin(\omega t - kx)$ and $y_2 = A_2 \sin(\omega t - kx - 	heta)$,where $A_1 = 2a$ and $A_2 = 2a$.Using th

Vedclass · Accepted Answer

$4a \cos(	heta / 2)$

Vedclass · Answer

(C) The given wave equations are $y_1 = A_1 \sin(\omega t - kx)$ and $y_2 = A_2 \sin(\omega t - kx - 	heta)$,where $A_1 = 2a$ and $A_2 = 2a$.Using the principle of superposition,the resultant amplitude $A_R$ for two waves with amplitudes $A_1$ and $A_2$ and phase difference $\phi$ is given by $A_R = \sqrt{A_1^2 + A_2^2 + 2A_1 A_2 \cos \phi}$.Here,$A_1 = A_2 = 2a$ and $\phi = 	heta$.$A_R = \sqrt{(2a)^2 + (2a)^2 + 2(2a)(2a) \cos 	heta}$$A_R = \sqrt{4a^2 + 4a^2 + 8a^2 \cos 	heta} = \sqrt{8a^2(1 + \cos 	heta)}$Using the identity $1 + \cos 	heta = 2 \cos^2(	heta / 2)$:$A_R = \sqrt{8a^2 \cdot 2 \cos^2(	heta / 2)} = \sqrt{16a^2 \cos^2(	heta / 2)}$$A_R = 4a \cos(	heta / 2)$.

Equations of motion for two waves traveling in the same direction are given by $y_1 = 2a \sin(\omega t - kx)$ and $y_2 = 2a \sin(\omega t - kx - \theta)$. The resultant amplitude of the medium particle will be:

Similar Questions

The equations of two waves are given as
$\begin{aligned}
& y_1=a \sin \left(\omega t+\phi_1\right) \\
& y_2=a \sin \left(\omega t+\phi_2\right)
\end{aligned}$
If the amplitude and time period of the resultant wave are the same as those of the individual waves,then $(\phi_1-\phi_2)$ is

Two waves are superimposed whose ratio of intensities is $9: 1$. The ratio of maximum and minimum intensity is

When two light waves each of amplitude $A$ and having a phase difference of $\frac{\pi}{2}$ are superimposed,the amplitude of the resultant wave is:

State the principle of superposition and explain it.

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module