The displacement associated with a standing wave on a sonometer is given by the following...

The displacement associated with a standing wave on a sonometer is given by the following equation:

If the length of the string is L then the allowed values of λ are 2L, 2L/2, 2L/3, … (see Sec. 13.2). Consider the case when λ = 2L/5; study the time variation of displacement in each loop and show that alternate loops vibrate in phase (with different points in a loop having different amplitudes) and adjacent loops vibrate out of phase.