amplitude of the wave.

since the sine function varies
between 1 and –1, 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 – ωt + φ) appearing as the
argument of the sine function in Eq. (15.2) is
called the phase of the wave. Given the
amplitude a, the phase determines the
displacement of the wave at any position and at
any instant. Clearly φ is the phase at x = 0 and
t = 0. Hence φ is called the initial phase angle.
By suitable choice of origin on the x-axis and
the intial time, it is possible to have φ = 0. Thus
there is no loss of generality in dropping φ, i.e.,
in taking Eq. (15.2) with φ = 0.