A wave travels uniformly in all directions fr | vedclass

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

Question

(B) For a spherical wave traveling uniformly in all directions from a point source,the energy is distributed over the surface area of a sphere,which i

Vedclass · Accepted Answer

$[A/r] \sin(kr - \omega t)$

Vedclass · Answer

(B) For a spherical wave traveling uniformly in all directions from a point source,the energy is distributed over the surface area of a sphere,which is $4\pi r^2$.Since the intensity $I$ is proportional to the square of the amplitude $a$ $(I \propto a^2)$ and intensity also follows the inverse square law $(I \propto 1/r^2)$,we have $a^2 \propto 1/r^2$,which implies $a \propto 1/r$.Therefore,the amplitude of the wave at a distance $r$ is given by $A/r$.Thus,the displacement of the medium at distance $r$ is represented by $y = \frac{A}{r} \sin(kr - \omega t)$.

$A$ wave travels uniformly in all directions from a point source in an isotropic medium. The displacement of the medium at any point at a distance $r$ from the source may be represented by ($A$ is a constant representing strength of source)

Similar Questions

$A$ 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

$A$ wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x - \frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ($y$ and $x$ are in metres and $t$ is in seconds).

If $\vec{u}$ is the instantaneous velocity of a particle and $\vec{v}$ is the velocity of the wave,then:

$A$ travelling wave pulse is given by $y = \frac{4}{3x^2 + 48t^2 + 24xt + 2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the wave is ........... $m/s$.

The equation of wave motion is $Y = 5 \sin (10 \pi t - 0.02 \pi x + \pi / 3)$ where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is (in $m/s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module