Two progressive transverse waves given by `y_(1) =0.007 sinpi ( 12x- 500 t )`and `y _(2) = 0.07 sin pi ( 12x+500t)` travelling along a stretched string from nodes and antinodes . What is the displacement at the (a) nodes (b) antinodes ? What is the wavelength of the standing wave ?

Explanation

`A_(1) = 0.07 ,A_(2) = 0.07 , K = 12pi `
(a) At nodes , displacement
`y= A_(1) -A_(2) = 0.07-0.07 =0`
(b) At antinodes ,displacement
`y =A_(1) + A_(2) = 0.07 +0.07 =0.14m`
(c ) Wavelength `lambda = ( 2pi)/( K ) = (2pi)/(12pi) = 0.16m`