A transverse wave in a medium is given by y = | vedclass

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

Question

(D) The given wave equation is $y = A \sin(2\omega t - 2kx)$.Comparing this with the standard wave equation $y = A \sin(\omega' t - k' x)$,we have ang

Vedclass · Accepted Answer

$\frac{\lambda}{4 \pi}$

Vedclass · Answer

(D) The given wave equation is $y = A \sin(2\omega t - 2kx)$.Comparing this with the standard wave equation $y = A \sin(\omega' t - k' x)$,we have angular frequency $\omega' = 2\omega$ and wave number $k' = 2k$.The velocity of the particle is $v_p = \frac{dy}{dt} = A \cdot (2\omega) \cos(2\omega t - 2kx)$.The maximum particle velocity is $v_{p,max} = 2A\omega$.The wave velocity is $v_w = \frac{\omega'}{k'} = \frac{2\omega}{2k} = \frac{\omega}{k}$.Given that $v_{p,max} = v_w$,we have $2A\omega = \frac{\omega}{k}$.Thus,$A = \frac{1}{2k}$.Since the wave number $k = \frac{2\pi}{\lambda}$,we substitute this into the expression for $A$:$A = \frac{1}{2(2\pi / \lambda)} = \frac{\lambda}{4\pi}$.

$A$ transverse wave in a medium is given by $y = A \sin 2(\omega t - kx)$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to the magnitude of the wave velocity. What is the value of $A$?

Similar Questions

The speed of a wave in a medium is $960 \, m/s$. If $3600$ waves pass through a point in the medium in $1 \, minute$,what is the wavelength of the wave in $meters$?

$A$ wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x) \} $ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

Two waves are represented by the equations $y_1 = A \sin (\omega t + kx + 0.57) \ m$ and $y_2 = A \cos (\omega t + kx) \ m$,where $x$ is in metre and $t$ is in second. What is the phase difference between them?

The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3}) \, \text{m}$,where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $\text{m/s}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module