The path difference between two waves Y_1 = a | vedclass

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

Question

(B) Given waves are $Y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $Y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \p

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given waves are $Y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}ight)$ and $Y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phiight)$.To compare the phases,we convert the cosine function to sine: $\cos(	heta) = \sin(	heta + \frac{\pi}{2})$.Thus,$Y_2 = a_2 \sin \left(\omega t - \frac{2 \pi x}{\lambda} + \phi + \frac{\pi}{2}ight)$.The phase difference $\delta$ is the difference between the arguments of the sine functions: $\delta = \left(\omega t - \frac{2 \pi x}{\lambda} + \phi + \frac{\pi}{2}ight) - \left(\omega t - \frac{2 \pi x}{\lambda}ight) = \phi + \frac{\pi}{2}$.The relationship between path difference $\Delta x$ and phase difference $\delta$ is $\Delta x = \frac{\lambda}{2 \pi} \delta$.Substituting the value of $\delta$,we get $\Delta x = \frac{\lambda}{2 \pi} \left(\phi + \frac{\pi}{2}ight)$.

The path difference between two waves $Y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $Y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phi\right)$ is

Similar Questions

If $\vec{u}$ is the instantaneous velocity of a particle and $\vec{v}$ is the velocity of the wave,then:

Consider the snapshot of a wave traveling in the positive $x$-direction.

If the equation of a transverse wave is $y = 5\sin 2\pi \left[ \frac{t}{0.04} - \frac{x}{40} \right]$,where distance is in $cm$ and time is in seconds,then the wavelength of the wave is .... $cm$.

Obtain the relation between wave velocity,angular frequency,and angular wave number.

$A$ boat at anchor is rocked by waves whose crests are $100 \ m$ apart and velocity is $25 \ m/s$. The boat bounces up once in every: ... $s$

Vedclass Test Series

Exam Paper Generator

Online Exam Module