largest possible value for A . For φ , the waves are completely, out of phase and the resultant wave has zero displacement everywhere at all times y ( x, t ) = ( . ) Eq. ( .
) refers to the so-called constructive interference of the two waves where the amplitudes add up in the resultant wave. Eq. ( . ) is the case of destructive intereference where the amplitudes subtract out in the resultant wave.
Fig. . shows these two cases of interference of waves arising from the principle of superposition. .
REFLECTION OF WAVES So far we considered waves propagating in an unbounded medium. What happens if a pulse or a wave meets a boundary? If the boundary is rigid, the pulse or wave gets reflected. The Fig.
. The resultant of two harmonic waves of equal amplitude and wavelength according to the principle of superposition. The amplitude of the resultant wave depends on the phase difference φ , which is zero for (a) and π for (b) If on the other hand, the boundary point is not rigid but completely free to move (such as in the case of a string tied to a freely moving ring on a rod), the reflected pulse has the same phase and amplitude (assuming no energy dissipation) as the incident pulse. The net maximum displacement at the boundary is then twice the amplitude of each pulse.
An example of non- rigid boundary is the open end of an organ pipe. To summarise, a travelling wave or pulse suffers a phase change of π on reflection at a rigid boundary and no phase change on reflection at an open boundary. To put this mathematically, let the incident travelling wave be ,