A transverse wave Y=2 sin (0.01 x+30 t) moves | vedclass

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(C) The given wave equation is $Y=2 \sin (0.01 x+30 t)$.Comparing this with the standard wave equation $Y=A \sin (kx+\omega t)$:We get the wave number

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) The given wave equation is $Y=2 \sin (0.01 x+30 t)$.Comparing this with the standard wave equation $Y=A \sin (kx+\omega t)$:We get the wave number $k = 0.01 \ cm^{-1}$ and angular frequency $\omega = 30 \ rad/s$.The wave velocity $v$ is given by $v = \frac{\omega}{k} = \frac{30}{0.01} = 3000 \ cm/s$.Converting the velocity to meters per second: $v = 30 \ m/s$.The length of the string $L$ is the distance traveled by the wave in time $t = 0.5 \ s$.$L = v 	imes t = 30 \ m/s 	imes 0.5 \ s = 15 \ m$.

$A$ transverse wave $Y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ in $s$,then the length of the string is: (in $m$)

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