The path difference between two waves,represe | vedclass

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

Question

(B) Given equations are:$y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$$y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \ph

Vedclass · Accepted Answer

$\frac{\lambda}{2 \pi}\left(\phi + \frac{\pi}{2}\right)$

Vedclass · Answer

(B) Given equations are:$y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}ight)$$y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phiight)$We know that $\cos 	heta = \sin \left(	heta + \frac{\pi}{2}ight)$.Therefore,$y_2$ can be rewritten as:$y_2 = a_2 \sin \left(\omega t - \frac{2 \pi x}{\lambda} + \phi + \frac{\pi}{2}ight)$The phase difference $\Delta \Phi$ between the two waves is the difference in their arguments:$\Delta \Phi = \left(\omega t - \frac{2 \pi x}{\lambda} + \phi + \frac{\pi}{2}ight) - \left(\omega t - \frac{2 \pi x}{\lambda}ight) = \phi + \frac{\pi}{2}$The relationship between path difference $\Delta x$ and phase difference $\Delta \Phi$ is given by:$\Delta x = \frac{\lambda}{2 \pi} 	imes \Delta \Phi$Substituting the value of $\Delta \Phi$:$\Delta x = \frac{\lambda}{2 \pi} \left(\phi + \frac{\pi}{2}ight)$

The path difference between two waves,represented by $y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phi\right)$ is

Similar Questions

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents a

The equation of a transverse wave travelling on a rope is given by $y = 10\sin \pi (0.01x - 2.00t)$ where $y$ and $x$ are in $cm$ and $t$ is in $seconds$. The maximum transverse speed of a particle in the rope is about .... $cm/s$.

Velocity of sound waves in air is $V \ m/s$. For a particular sound wave in air,a path difference of $x \ cm$ is equivalent to a phase difference of $n\pi$. The frequency of this wave is:

The equation of a progressive wave is $y = a \sin(200t - x)$,where $x$ is in meters and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

$A$ transverse wave propagates in a medium with a velocity of $1450 \, m/s$. The distance between the nearest points at which the oscillations of the particles are in the opposite phase (phase difference of $\pi$) is $0.1 \, m$. What is the frequency of the wave in $Hz$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module