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

The speed of a wave in a certain medium is $960 \,m/s$. If $900$ waves pass over a certain point of the medium in half a minute, the wavelength of the wave is (in $\,m$)

If a given wave has a propagation constant of $\frac{5 \pi}{7} \, rad/m$,then the phase difference between two particles having a distance difference of $\frac{49}{22} \, m$ is ..... $rad.$ (Take $\pi = \frac{22}{7}$)

The wave function of a pulse is given by $y = \frac{5}{(4x + 6t)^2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the pulse is ......... $m/s$.

The equation of a sound wave is $y = 0.0015 \sin (62.4x + 316t)$. The wavelength of this wave is ..... $unit$.

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

Vedclass Test Series

Exam Paper Generator

Online Exam Module