Write the equation of a wave identical to the wave represented by the equation `y=5sinpi(4.0t-0.02x)`, but moving in opposite direction. Write the equation of stationary wave produced by the combination of these two waves. Determine the distance between two nearest nodes. All distances in the equations are in mm.

Explanation

The given eqn. is
`y=5sinpi(4.0t-0.02x)`
The wave with the same parameters travelling in opposite direction is `y^(')=5sinpi(4.0t+0.02x)`.
The wave with the same parameters travelling in opposite direction is `y^(')=5sinpi(4.0t+0.02x)`.
As `Y=y+y^(')=5sinpi(4.0t-0.02x)`
`+5sinpi(4.0t+0.02x)`
`=5sin[(4pit-0.02pix+4pit+0.02x)/(2)]`
`cos[(4pit+0.02pix-4pit+0.02x)/(2)]`
`y=5sin4pitcos0.02pix`
This is the equation of stationary wave.
Here, `k=(2pi)/(lambda)=0.02pi,`
`lambda=(2pi)/(0.02pi)=100mm`
Distance between two nearest nodes,
`(lambda)/(2)=50mm`