The equation of a transverse wave is given by | vedclass

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

Question

(B) Given equation: $y=0.05 \sin \pi(2 t-0.02 x)$ Expanding the equation: $y=0.05 \sin (2 \pi t - 0.02 \pi x)$ Comparing this with the standard wave e

Vedclass · Accepted Answer

$100 \ m, 100 \ ms^{-1}$

Vedclass · Answer

(B) Given equation: $y=0.05 \sin \pi(2 t-0.02 x)$ Expanding the equation: $y=0.05 \sin (2 \pi t - 0.02 \pi x)$ Comparing this with the standard wave equation $y=a \sin (\omega t - k x)$: Angular frequency $\omega = 2 \pi \ rad/s$ Wave number $k = 0.02 \pi \ m^{-1}$ The minimum distance between two particles in phase is the wavelength $\lambda$. Since $k = \frac{2 \pi}{\lambda}$,we have $\lambda = \frac{2 \pi}{k} = \frac{2 \pi}{0.02 \pi} = \frac{2}{0.02} = 100 \ m$. The wave velocity $v$ is given by $v = \frac{\omega}{k}$. $v = \frac{2 \pi}{0.02 \pi} = \frac{2}{0.02} = 100 \ m/s$.

The equation of a transverse wave is given by $y=0.05 \sin \pi(2 t-0.02 x)$,where $x, y$ are in metre and $t$ is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively

Similar Questions

$A$ body sends a wave $150 \text{ mm}$ long through medium $P$ and $0.30 \text{ m}$ long in medium $Q$. If velocity of the wave in medium $P$ is $80 \text{ cm s}^{-1}$, the velocity of wave in medium $Q$ is (in $\text{ m s}^{-1}$)

The number of waves contained in unit length of the medium is called

$A$ wave is propagating along the $x$-axis. The displacement of particles of the medium in the $z$-direction at $t = 0$ is given by: $z = \exp[-(x + 2)^2]$,where $x$ is in meters. At $t = 1 \ s$,the same wave disturbance is given by: $z = \exp[-(2 - x)^2]$. Then,the wave propagation velocity is:

$A$ sine wave has an amplitude $A$ and wavelength $\lambda$. Let $V$ be the wave velocity and $v$ be the maximum velocity of a particle in the medium. Then:

$A$ longitudinal wave is represented by $x=x_0 \sin 2 \pi(n t-x / \lambda)$. The maximum particle velocity will be four times the wave velocity if:

Vedclass Test Series

Exam Paper Generator

Online Exam Module