Question

The standing wave in a medium is expressed as y = 0.2 sin (0.8 x) cos (3000 t) m. The distance between any two consecutive points of minimum or maximum displacement is

Answer 1

Answer:$\lambda = \dfrac{5\pi}{2}\ m$.

Explanation:

Given that,

$y = 0.2 sin (0.8x)\ cos (3000 t) m$

We know the general equation

$y = (2Acos\omega\ t)\ sin (kx)$

On comparing,

k = 0.8

We know that,

$\lambda = \dfrac{2\pi}{k}$

$\lambda = \dfrac{2\pi}{0.8}$

$\lambda = \dfrac{5\pi}{2}\ m$

Hence, the distance between two consecutive points of wave is $\lambda = \dfrac{5\pi}{2}\ m$.