To understand the concept of nodes of a standing wave. the nodes of a standing wave are points where the displacement of the wave is zero at all times. nodes are important for matching boundary conditions, for example that the point at which a string is tied to a support has zero displacement at all times (i. e., the point of attachment does not move). consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. here is a common mathematical form for such a wave:
y(x, t) = acos(x, t)sin(wt)

where a is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency of the wave, and t is time.
at which three points x1, x2 and x3 closest to x=0 but with x> 0, will the displacement of the string be zero for all times? these are the first three nodal points. express the first three nonzero nodal points as multiples of the wavelength lambda, using constants like pie . list the factors that multiply in increasing order, separated by commas.