Question

Two travelling waves, y₁ = A sin [k (x + ct)] and y₂ = A sin [k (x - ct)] are superposed on a string. The distance between adjacent nodes is ____________.

Options

• `("ct")/pi`

• `("ct")/(2pi)`

• `pi/(2"k")`

• `pi/"k"`

Answer 1

Two travelling waves, y₁ = A sin [k (x + ct)] and y₂ = A sin [k (x - ct)] are superposed on a string. The distance between adjacent nodes is `pi/"k"`.

Explanation:

`"Distance between adjacent nodes" = lambda//2`

`"Also"  (2pi)/lambda = "coefficient of x in the argument of the sine function" = "k" or lambda = (2pi)/"k"`

`therefore  "The distance between adjacent nodes" = pi/"k"`