In a stationary wave,all particles are

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

Question

(A) In a stationary wave,the displacement of any particle is given by $y = A \sin(kx) \cos(\omega t)$.For the particles to be at rest,the velocity $v

Vedclass · Accepted Answer

At rest at the same time twice in every period of oscillation

Vedclass · Answer

(A) In a stationary wave,the displacement of any particle is given by $y = A \sin(kx) \cos(\omega t)$.For the particles to be at rest,the velocity $v = \frac{dy}{dt} = -A \omega \sin(kx) \sin(\omega t)$ must be zero.This condition is satisfied when $\sin(\omega t) = 0$,which occurs at $\omega t = 0, \pi, 2\pi, \dots$Since $\omega = \frac{2\pi}{T}$,the condition $\sin(\omega t) = 0$ implies $t = 0, \frac{T}{2}, T, \dots$Thus,all particles in the medium come to rest simultaneously twice in every period of oscillation $T$.Therefore,option $A$ is correct.

Column - $A$	Column - $B$
$(a)$ Minimum change in pressure	$(i)$ Antinodal point
$(b)$ Maximum change in pressure	$(ii)$ Nodal point

Similar Questions

In case of a stationary wave pattern,which of the following statements is $CORRECT$?

Write the amplitude and phase difference for all particles of the same interval for stationary waves.

$A$ wave $y = a \cos(kx - \omega t)$ superposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

Match Column - $A$ with Column - $B$.

Column - $A$ Column - $B$

$(a)$ Minimum change in pressure $(i)$ Antinodal point

$(b)$ Maximum change in pressure $(ii)$ Nodal point

Vedclass Test Series

Exam Paper Generator

Online Exam Module