If the equation of a transverse wave is Y = 2 | vedclass

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

Question

(A) The standard equation of a transverse wave is given by $Y = a \sin(kx - \omega t)$.Comparing the given equation $Y = 2 \sin(kx - 2t)$ with the sta

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) The standard equation of a transverse wave is given by $Y = a \sin(kx - \omega t)$.Comparing the given equation $Y = 2 \sin(kx - 2t)$ with the standard form,we get the amplitude $a = 2$ and the angular frequency $\omega = 2$.The particle velocity $v_p$ is the derivative of displacement $Y$ with respect to time $t$:$v_p = \frac{dY}{dt} = \frac{d}{dt} [2 \sin(kx - 2t)] = 2 \cos(kx - 2t) 	imes (-2) = -4 \cos(kx - 2t)$.The maximum particle velocity is given by the magnitude of the coefficient of the cosine term:$v_{max} = a \omega = 2 	imes 2 = 4 \, units$.

If the equation of a transverse wave is $Y = 2 \sin(kx - 2t)$,then the maximum particle velocity is .... $units$.

Similar Questions

The graph between wave number $(\bar \nu)$ and angular frequency $(\omega)$ is

The distance between two consecutive crests in a wave train produced in a string is $5 \ cm$. If $2$ complete waves pass through any point per second,the velocity of the wave is ..... $cm/sec$.

$A$ sound wave of frequency $245 \,Hz$ travels with the speed of $300 \,ms^{-1}$ along the positive $x$-axis. Each point of the wave moves to and fro through a total distance of $6 \,cm$. What will be the mathematical expression of this travelling wave?

The figure shows the shape of a part of a long string in which transverse waves are produced by attaching one end of the string to a tuning fork of frequency $250 \ Hz$. What is the velocity of the waves in $ms^{-1}$?

The figure shows the wave $y = A \sin(\omega t - kx)$. What is the magnitude of the slope of the curve at $B$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module