A sound wave of frequency 245 ,Hz travels wit | vedclass

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

Question

(A) The general equation for a travelling wave is $Y(x, t) = A \sin(kx - \omega t)$.Given frequency $f = 245 \,Hz$,speed $v = 300 \,ms^{-1}$,and total

Vedclass · Accepted Answer

$Y(x, t)=0.03 \sin(5.1 x - 1.5 	imes 10^{3} t)$

Vedclass · Answer

(A) The general equation for a travelling wave is $Y(x, t) = A \sin(kx - \omega t)$.Given frequency $f = 245 \,Hz$,speed $v = 300 \,ms^{-1}$,and total path length (peak-to-peak) $= 6 \,cm$.Amplitude $A = \frac{6 \,cm}{2} = 3 \,cm = 0.03 \,m$.Angular frequency $\omega = 2 \pi f = 2 	imes 3.14 	imes 245 \approx 1538.6 \,rad/s \approx 1.5 	imes 10^{3} \,rad/s$.Wave number $k = \frac{\omega}{v} = \frac{1538.6}{300} \approx 5.12 \,m^{-1} \approx 5.1 \,m^{-1}$.Substituting these values,the equation is $Y(x, t) = 0.03 \sin(5.1 x - 1.5 	imes 10^{3} t)$.

$A$ 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?

Similar Questions

$A$ longitudinal wave is represented by $x=x_0 \sin 2 \pi(n t-x / \lambda)$. The maximum particle velocity will be four times the wave velocity if:

$A$ simple harmonic progressive wave is represented by $y=A \sin (100 \pi t+3 x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3}$ radian is

The equation $y = A \cos^2 \left( 2\pi nt - 2\pi \frac{x}{\lambda} \right)$ represents a wave with

In the wave equation $y = 0.5 \sin \frac{2 \pi}{\lambda}(400 t - x ) \, m$,the velocity of the wave will be ......... $m/s$.

$A$ transverse wave is represented by $y = 2 \sin(\omega t - kx) \ cm$. The value of wavelength (in $cm$) for which the wave velocity becomes equal to the maximum particle velocity is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module