Question

A progressive wave is given by
y=3 sin 2pi [(t//0.04)-(x//0.01)]
where x, y are in cm and t in s. the frequency of wave and maximum accelration will be:

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Frequency=25\:Hertz}}}$

$\green{\tt{\therefore{Max\:acc^{n}=- 3 \: (\frac{4\pi^{2} }{0.0016})\:m/s^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green {\underline \bold{given: }} \\ \tt: \implies y = 3 \: sin \: 2\pi( (\frac{t}{0.04} ) - (\frac{x}{0.01} )) \\ \\ \red{\underline \bold{to \: find: }} \\ \tt: \implies frequency = ? \\ \\ \tt: \implies maximum \: acceleration =?$

• According to given question :

$\tt: \implies 3 \: sin \: 2\pi(( \frac{t}{0.04}) - ( \frac{x}{0.01} )) \\ \\ \tt: \implies 3 \: sin(( \frac{2\pi t}{0.04}) - (\frac{2\pi x}{0.01} ) \\ \\ \tt \circ \: amplitude = 3 \\ \\ \tt\circ \: \omega = \frac{2\pi}{0.04} \\ \\ \tt \circ \: k = \frac{2\pi}{0.01} \\ \\ \bold{as \: we \: know \: that} \\ \tt: \implies f= \frac{1}{t} \\ \\ \tt: \implies f = \frac{1}{ \frac{2\pi}{ \omega} } \\ \\ \tt: \implies f = \frac{ \omega}{2\pi} \\ \\ \tt: \implies f = \frac{ \frac{2\pi}{0.04} }{2\pi} \\ \\ \green{\tt: \implies f = \frac{1}{0.04}\:Hertz } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies acceleration = - a { \omega}^{2} \: sin( \omega t - kx) \\ \\ \tt: \implies a = - 3 \: (\frac{2\pi}{0.04} )^{2} \: sin(( \frac{2\pi}{0.04} \times t - \frac{2\pi}{0.01}x)) \\ \\ \green{ \tt: \implies a = - 3 \: (\frac{4\pi^{2} }{0.0016} \: )sin( \frac{2\pi \: t}{0.04} - \frac{2\pi x}{0.01} )}\\\\ \text{For\:maximum\:acceleration\:sin\:value\:should\:be\:1} \\ \green{\tt:\implies Max\:acc^{n}=-3\:(\frac{4\pi^{2}}{0.0016})\:m/s^{2}}$