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

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(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?

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