Question

A Sound wave with an amplitude of $3cm$ starts moving towards right from origin and gets reflected at a rigid wall after a second. If the velocity of the wave is $340m{s}^{-1}$ and it has a wavelength of $2m$, the equations of incident and reflected waves are

• A. $y=3\times {10}^{-2}\sin \pi (340t-x),y=-3\times {10}^{-2}\sin \pi (340t+x)$ towards left
• B. $y=4\times {10}^{-2}\sin \pi (340t+x),y=-4\times {10}^{-2}\sin \pi (340t+x)$ towards left
• C. $y=5\times {10}^{-2}\sin \pi (340t-x),y=-5\times {10}^{-2}\sin \pi (340t-x)$ towards left
• D. $y=6\times {10}^{-2}\sin \pi (340t-x),y=-6\times {10}^{-2}\sin \pi (340t+x)$ towards left

Answer 1

The correct option is A $y=3\times {10}^{-2}\sin \pi (340t-x),y=-3\times {10}^{-2}\sin \pi (340t+x)$ towards left

$A=3cm$
$y=A\sin (Vt-x)$
$V=\lambda /t$
$f=170sec$
$y_1=A\sin (Vt-x)$
$y_2=A\sin (Vt+x)$
$\therefore y_1=3\times {10}^{-2}\sin k(340t-x),$
$y_2=3\times {10}^{-2}\sin k(340t+x)$
$k=\frac{2\pi }{\lambda }$
$k=\frac{2\pi }{2}$
$k=\pi$
$\therefore y_1=3\times {10}^{-2}\sin \pi (340t-x)$
$y_2=3\times {10}^{-2}\sin \pi (340t+x)$