y x t

y x t ( . ) represents a wave travelling in the negative direction of x -axis. Fig. ( . ) gives the names of the various physical quantities appearing in Eq. ( . ) that we now interpret. Fig. . shows the plots of Eq. ( . ) for different values of time differing by equal intervals of time. In a wave, the crest is the point of maximum positive displacement, the trough is the point of maximum negative displacement. To see how a wave travels, we can fix attention on a crest and see how it progresses with time. In the figure, this is shown by a cross (×) on the crest. In the same manner, we can see the motion of a particular constituent of the medium at a fixed location, say at the origin of the x -axis. This is shown by a solid dot (•). The plots of Fig. . show that with time, the solid dot (•) at the origin moves periodically, i.e., the particle at the origin oscillates about its mean position as the wave progresses. This is true for any other location also. We also see that during the time the solid dot (•) has completed one full oscillation, the crest has moved further by a certain distance. Using the plots of Fig. . , we now define the various quantities of Eq. ( . ). . . Amplitude and Phase In Eq. ( . ), since the sine function varies between and – , the displacement y ( x,t ) varies between a and – a . We can take a to be a positive constant, without any loss of generality. Then, a represents the maximum displacement of the constituents of the medium from their equilibrium position. Note that the displacement y may be positive or negative, but a is positive. It is called the amplitude of the wave. The quantity ( kx – ω t + φ ) appearing as the argument of the sine function in Eq. ( . ) is called the phase of the wave. Given the amplitude a , the phase determines the displacement of the wave at any position and at