Waves on "commutative" spacetimes like R-d are elements of the commutative algebra C-0(R-d) of functions on R-d. When C-0(R-d) is deformed to a noncommutative algebra A(theta)(R-d) with deformation parameter theta (A(0)(R-d)=C-0(R-d)), waves being its elements, are no longer complex-valued functions on R-d. Rules for their interpretation, such as measurement of their intensity, and energy, thus need to be stated. We address this task here. We then apply the rules to interference and diffraction for d <= 4 and with time-space noncommutativity. Novel phenomena are encountered. Thus when the time of observation T is so brief that T <= 2 theta w, where w is the frequency of incident waves, no interference can be observed. For larger times, the interference pattern is deformed and depends on theta w/T. It approaches the commutative pattern only when theta w/T -> 0. As an application, we discuss interference of starlight due to cosmic strings.