A wave travelling along the x-axis is describ | vedclass

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

Question

(A) The general equation of a travelling wave is given by $y(x, t) = A \cos(kx - \omega t)$.Comparing this with the given equation $y(x, t) = 0.005 \c

Vedclass · Accepted Answer

$\alpha = 25.00\pi, \beta = \pi$

Vedclass · Answer

(A) The general equation of a travelling wave is given by $y(x, t) = A \cos(kx - \omega t)$.Comparing this with the given equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$,we identify $\alpha = k$ and $\beta = \omega$.The wave number $k$ is related to the wavelength $\lambda$ by the formula $k = \frac{2\pi}{\lambda}$.Given $\lambda = 0.08 \ m$,we have $\alpha = k = \frac{2\pi}{0.08} = 25\pi \ m^{-1}$.The angular frequency $\omega$ is related to the time period $T$ by the formula $\omega = \frac{2\pi}{T}$.Given $T = 2.0 \ s$,we have $\beta = \omega = \frac{2\pi}{2.0} = \pi \ rad/s$.Thus,$\alpha = 25\pi$ and $\beta = \pi$.

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$ respectively,then $\alpha$ and $\beta$ in appropriate units are:

Similar Questions

The equation of a progressive wave is $y = a \sin \left( \frac{\pi}{2}x - 200\pi t \right)$. The frequency of the wave will be .... $Hz$.

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 $^{\circ}$)

In a wave motion $y = a \sin (kx - \omega t)$,$y$ can represent

Two waves are given by $y_1 = a \sin(\omega t - kx)$ and $y_2 = a \cos(\omega t - kx)$. The phase difference between the two waves is

Vedclass Test Series

Exam Paper Generator

Online Exam Module