A wave is given by Y = 3 sin 2 pi left( frac{ | vedclass

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(D) The given wave equation is $Y = 3 \sin 2 \pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$.Comparing this with the standard wave equation $Y = A

Vedclass · Accepted Answer

$25 \ Hz, 7.5 	imes 10^4 \ cm/s^2$

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(D) The given wave equation is $Y = 3 \sin 2 \pi \left( \frac{t}{0.04} - \frac{x}{0.01} ight)$.Comparing this with the standard wave equation $Y = A \sin 2 \pi \left( ft - \frac{x}{\lambda} ight)$,we get the frequency $f = \frac{1}{0.04} = 25 \ Hz$.The angular frequency is $\omega = 2 \pi f = 2 \pi 	imes 25 = 50 \pi \ rad/s$.The maximum acceleration $a_{\max}$ is given by $a_{\max} = \omega^2 A$.Substituting the values: $a_{\max} = (50 \pi)^2 	imes 3 = 2500 	imes \pi^2 	imes 3$.Given $\pi^2 = 10$,we have $a_{\max} = 2500 	imes 10 	imes 3 = 75000 \ cm/s^2 = 7.5 	imes 10^4 \ cm/s^2$.

$A$ wave is given by $Y = 3 \sin 2 \pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$ where $Y$ is in $cm$. The frequency of the wave and the maximum acceleration will be $(\pi^2 = 10)$.

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