A transverse wave in a medium is described by | vedclass

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

Question

(A) The given wave equation is $y = A \sin^2 (\omega t - kx)$.Using the trigonometric identity $\sin^2 	heta = \frac{1 - \cos(2	heta)}{2}$,we can re

Vedclass · Accepted Answer

$\lambda / 2\pi$

Vedclass · Answer

(A) The given wave equation is $y = A \sin^2 (\omega t - kx)$.Using the trigonometric identity $\sin^2 	heta = \frac{1 - \cos(2	heta)}{2}$,we can rewrite the equation as:$y = \frac{A}{2} [1 - \cos(2\omega t - 2kx)]$.The particle velocity $v_p$ is given by the derivative of $y$ with respect to time $t$:$v_p = \frac{\partial y}{\partial t} = \frac{A}{2} [2\omega \sin(2\omega t - 2kx)] = A\omega \sin(2\omega t - 2kx)$.The maximum particle velocity is $(v_p)_{\max} = A\omega$.The wave velocity $v$ is given by the ratio of the coefficient of $t$ to the coefficient of $x$ in the argument of the function:$v = \frac{2\omega}{2k} = \frac{\omega}{k}$.Since $k = \frac{2\pi}{\lambda}$,we have $v = \frac{\omega}{2\pi / \lambda} = \frac{\omega \lambda}{2\pi}$.According to the problem,$(v_p)_{\max} = v$:$A\omega = \frac{\omega \lambda}{2\pi}$.Solving for $A$,we get $A = \frac{\lambda}{2\pi}$.

$A$ transverse wave in a medium is described by the equation $y = A \sin^2 (\omega t - kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to that of the wave velocity,if the value of $A$ is ($\lambda$ = wavelength of wave).

Similar Questions

$A$ wave is given by $y = 3 \sin 2\pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$,where $y$ is in $cm$. The frequency of the wave and the maximum acceleration of the particle are:

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)

$A$ wave travelling in the $+ve$ $x$-direction having displacement along $y$-direction as $1\, m$,wavelength $2\pi\, m$,and frequency of $\frac{1}{\pi}\ Hz$ is represented by

The equation of a transverse wave is given by $y = 100 \sin \pi (0.04z - 2t)$,where $y$ and $z$ are in $cm$ and $t$ is in seconds. The frequency of the wave in $Hz$ is

An equation of a simple harmonic progressive wave is given by $y=A \sin (100 \pi t-3 x)$. The distance between two particles having a phase difference of $\frac{\pi}{18}$ in meters is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module