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

$A$ transverse wave propagating along the $x-$ axis is represented by $y(x,t) = 8.0 \sin \left( 0.5\pi x - 4\pi t - \frac{\pi}{4} \right)$,where $x$ is in metres and $t$ is in seconds. The speed of the wave is ..... $m/s$.

The equation of a travelling wave is given by $y = 0.5 \sin(20x - 400t)$,where $x$ and $y$ are in meters and $t$ is in seconds. The velocity of the wave is .... $m/s$.

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

When a sound wave of wavelength $\lambda$ is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

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