# What is Standing or stationary waves?

When two harmonic waves of equal frequency and amplitude travelling through a medium (say string) in opposite directions superimpose each other, we get stationary waves. Suppose the two waves are

${{y}_{1}}=Asin left( kx-omega t right)$ and ${{y}_{2}}=Asin left( kx+omega t right)$

By the principle of superposition their sum is

$y={{y}_{1}}+{{y}_{2}}$

or $y=Aleft[ sin left( kx-omega t right)+sin left( kx+omega t right) right]$

By using the identity,

$sin A+sin B=2sin left( frac{A+B}{2} right)cos left( frac{A-B}{2} right),$

We obtain $y=2Asin left( kx right)cos left( omega t right)$

Or $y=2Asin left( frac{2pi x}{lambda } right)cos left( frac{2pi t}{T} right)$