A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, yx, t=0.5sin⁡(5π)/4xcos⁡200πt. What is the speed of the travelling wave moving in the positive x direction? (x and t are in meter and second, respectively)

Correct answer: (C) 160 m s^(-1). y=2asinkxcosωt ⇒k=(5π)/4 m^(-1), ω=200π rad s^(-1), v=(ω)/k=(200π)/(5π4)=160 m s^(-1)

Q75 / 90 · JEE Main 2017 (09 Apr Online) · Physics

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, $y (x, t) = 0.5 \sin (\frac{5 π}{4} x) \cos (200 π t)$ . What is the speed of the travelling wave moving in the positive $x$ direction? ( $x$ and $t$ are in meter and second, respectively)

y = 2 a \sin (k x) \cos (ω t)

\Rightarrow k = \frac{5 π}{4} m^{- 1}, ω = 200 π rad s^{- 1}

v = \frac{ω}{k}

= \frac{200 π}{\frac{5 π}{4}} = 160 m s^{- 1}

Hence, the correct answer is option: 'C'.