Question

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?

Answer 1

Answer:

The wavelength of the interfering waves is 3.14 meters.

Explanation:

Given that,

The equation of standing wave that is formed by interfering two harmonic waves (travelling opposite direction) is given by :

$y=3\ sin(2x)\ cos(5t)$........(1)

The general equation of standing wave is given by :

$y=2A\ sin(kx)\ cos(\omega t)$..............(2)

On comparing equation (1) and (2), we get :

k = 2

We know that,

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

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

$\lambda=3.14\ m$

So, the wavelength of the interfering wave is 3.14 meters. Hence, this is the required solution.