Two waves are represented by: x_1 = A sin lef | vedclass

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

Question

(B) Given the equations for the two waves are $x_1 = A \sin \left(\omega t + \frac{\pi}{6}\right)$ and $x_2 = A \cos \omega t$.To find the phase diffe

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(B) Given the equations for the two waves are $x_1 = A \sin \left(\omega t + \frac{\pi}{6}ight)$ and $x_2 = A \cos \omega t$.To find the phase difference,we express both waves in terms of the same trigonometric function (sine or cosine).We know that $\cos 	heta = \sin \left(	heta + \frac{\pi}{2}ight)$.Therefore,$x_2 = A \sin \left(\omega t + \frac{\pi}{2}ight)$.Now,the phase of $x_1$ is $\phi_1 = \omega t + \frac{\pi}{6}$ and the phase of $x_2$ is $\phi_2 = \omega t + \frac{\pi}{2}$.The phase difference $\Delta \phi = \phi_2 - \phi_1 = \left(\omega t + \frac{\pi}{2}ight) - \left(\omega t + \frac{\pi}{6}ight)$.$\Delta \phi = \frac{\pi}{2} - \frac{\pi}{6} = \frac{3\pi - \pi}{6} = \frac{2\pi}{6} = \frac{\pi}{3}$.

Two waves are represented by: $x_1 = A \sin \left(\omega t + \frac{\pi}{6}\right)$ and $x_2 = A \cos \omega t$. Then the phase difference between them is

Similar Questions

What is the phase difference between consecutive crest and trough?

The relation between phase difference $(\Delta \phi)$ and path difference $(\Delta x)$ is:

$A$ plane wave is described by the equation $y = 3 \cos \left( \frac{x}{4} - 10t - \frac{\pi}{2} \right)$. The maximum velocity of the particles of the medium due to this wave is

The equation of a wave travelling along the positive $x$-axis,as shown in the figure at $t = 0$,is given by:

$A$ transverse wave is represented by $y = A \sin(\omega t - kx)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module