Question

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

• A. $\begin{array}{c}y=3\times {10}^{-2}\sin \pi (340t-x)\\ y=-3\times {10}^{-2}\sin \pi (340t+x)\text{towards left}\end{array}$
• B. $\begin{array}{c}y=3\times {10}^{-2}\sin \pi (340t+x)\\ y=-3\times {10}^{-2}\sin \pi (340t+x)\text{towards left}\end{array}$
• C. $\begin{array}{c}y=3\times {10}^{-2}\sin \pi (340t-x)\\ y=-3\times {10}^{-2}\sin \pi (340t-x)\text{towards left}\end{array}$
• D. $\begin{array}{c}y=3\times {10}^2\sin \pi (340t-x)\\ I=3\times {10}^{-2}\sin \pi (340t+x)\text{towards left}\end{array}$

Answer 1

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

$\begin{array}{c}y=\left(3\times {10}^{-2}\right)\sin \left(\omega t-kx\right)\\ \lambda =2m=\frac{2\pi }{k}\\ \Rightarrow k=\pi \\ v=340m/s\\ w=vk\\ =240\pi \\ Now,\\ y=\left(3\times {10}^{-2}\right)\sin \left(340\pi t-\pi x\right)towardsright\\ and,\\ y=\left(3\times {10}^{-2}\right)\sin \left(340\pi t+\pi x+\pi \right)\\ =-\left(3\times {10}^{-2}\right)\sin \left(340\pi t+\pi x\right)towardsleft\\ Hence,theoptionAisthecorrectanswer.\end{array}$