In a standing wave on a string rigidly fixed | vedclass

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

Question

(C) In a standing wave, the displacement of any particle at position $x$ is given by $y(x, t) = A(x) \sin(\omega t + \phi)$.All particles in a given l

Vedclass · Accepted Answer

in one time period all the particles are simultaneously at rest twice.

Vedclass · Answer

(C) In a standing wave, the displacement of any particle at position $x$ is given by $y(x, t) = A(x) \sin(\omega t + \phi)$.All particles in a given loop oscillate with the same phase, but particles in adjacent loops oscillate with a phase difference of $\pi$.At the extreme positions, all particles in a specific loop reach their maximum displacement simultaneously.However, because adjacent loops are out of phase, when particles in one loop are at their positive extreme, particles in the adjacent loop are at their negative extreme.Thus, all particles in the string are never at their positive extremes simultaneously.Conversely, all particles pass through their mean position (where they are momentarily at rest in terms of displacement, though velocity is maximum) twice in one time period $T$.Specifically, at $t = 0, T/2, T, \dots$, the entire string is momentarily straight (displacement $y = 0$ for all $x$).Therefore, in one time period, all particles are simultaneously at rest (at their mean position) twice.

In a standing wave on a string rigidly fixed at both ends:

Similar Questions

Standing waves can be produced:

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40\pi t$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is..... $cm$.

$A$ standing wave pattern is formed on a string. One of the waves is given by the equation $y_1 = a \cos(\omega t - kx + \pi/3)$. Find the equation of the other wave such that at $x = 0$,a node is formed.

Vedclass Test Series

Exam Paper Generator

Online Exam Module