A sinusoidal progressive wave is generated in | vedclass

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

Question

(C) The equation of the wave is $y = 2 \sin(2\pi x - 100\pi t + \pi/3)$.For the particle to be at the mean position,the displacement $y$ must be $0$.S

Vedclass · Accepted Answer

$\frac{1}{300} 	ext{ s}$

Vedclass · Answer

(C) The equation of the wave is $y = 2 \sin(2\pi x - 100\pi t + \pi/3)$.For the particle to be at the mean position,the displacement $y$ must be $0$.So,$2 \sin(2\pi x - 100\pi t + \pi/3) = 0$.This implies the argument of the sine function must be an integer multiple of $\pi$,i.e.,$2\pi x - 100\pi t + \pi/3 = n\pi$,where $n$ is an integer.Given $x = 4 	ext{ m}$,we substitute this into the equation:$2\pi(4) - 100\pi t + \pi/3 = n\pi$$8\pi - 100\pi t + \pi/3 = n\pi$$100\pi t = 8\pi + \pi/3 - n\pi = \frac{25\pi}{3} - n\pi$.To find the first time $t > 0$,we choose $n$ such that $t$ is positive and minimal. For $n = 8$:$100\pi t = \frac{25\pi}{3} - 8\pi = \frac{\pi}{3}$.$t = \frac{\pi/3}{100\pi} = \frac{1}{300} 	ext{ s}$.

$A$ sinusoidal progressive wave is generated in a string. Its equation is given by $y = (2 \text{ mm}) \sin(2\pi x - 100\pi t + \pi/3)$. The time when the particle at $x = 4 \text{ m}$ first passes through the mean position will be:

Similar Questions

The diagram shows the propagation of a progressive wave. $A$,$B$,$C$,$D$,$E$,and $F$ are points on this wave. Which of the following points are in the same state of vibration (i.e.,in the same phase)?

$A$ progressive wave is given by $Y = 12 \sin (5t - 4x)$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

The equation of a progressive wave is given by $y = 0.5 \sin(10t + x) \text{ m}$. What is the wave velocity in $\text{m/s}$?

$y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)$ represents an equation of a progressive wave,where $t$ is in $s$ and $x$ is in $m$. The distance travelled by the wave in $5 \,s$ is (in $\,m$)

The equation of a progressive wave is given by $y = 0.2 \cos \pi (0.04t + 0.02x - \frac{\pi}{6})$. The distance is expressed in $cm$ and time in seconds. What will be the minimum distance between two particles having a phase difference of $\pi / 2$ in $cm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module