Question

If two waves are represented by $y_1=2sin(4x-300t)$ and $y_2=sin(4x-300t-0.2)$ then, their superposed wave will have angular frequency

• A. $150/\pi$
• B. $150\pi$
• C. $300$
• D. $600\pi$

Answer 1

The correct option is C $300$

Given - $y_1=2\sin (4x-300t)$ and $y_2=\sin (4x-300t-0.2)$ ,

due to superposition resultant displacement will be ,

$y=y_1+y_2$ ,

or $y=2\sin (4x-300t)+\sin (4x-300t-0.2)$ ,

or $y=2\sin (4x-300t)+\sin (4x-300t)\cos \left(0.2\right)-\cos (4x-300t)\sin \left(0.2\right)$ ,

or $y=\sin (4x-300t)(2+\cos (0.2\left)\right)-\cos (4x-300t)\sin \left(0.2\right)$ ,

let $2+\cos \left(0.2\right)=A\cos \theta$ ,

$\sin \left(0.2\right)=A\sin \theta$ ,

where $A$ and $\theta$ are constants ,

then $y=A\sin (4x-300t)\cos \theta -A\cos (4x-300t)\sin \theta$ ,

or $y=A\sin (4x-300t-\theta )$ ,

comparing above equation with $y=a\sin (kx-\omega t)$

the angular frequency of this equation will be ,

$\omega t=300t$ ,

or $\omega =300rad/s$