travelling wave

For mathematical description of a travelling
wave, we need a function of both position x and
time t. Such a function at every instant should
give the shape of the wave at that instant. Also
at every given location, it should describe the
motion of the constituent of the medium at that
location. If we wish to describe a sinusoidal
travelling wave (such as the one shown in Fig.
15.3) the corresponding function must also be
sinusoidal. For convenience, we shall take the
wave to be transverse so that if the position of
the constituents of the medium is denoted by x,
the displacement from the equilibrium position
may be denoted by y. A sinusoidal travelling
wave is then described by :

y(x,t) asin(kx t ) (15.2)
The term φ in the argument of sine function
means equivalently that we are considering a
linear combination of sine and cosine functions:
y(x,t ) A sin(kx t ) Bcos(kx t ) (15.3)
From Equations (15.2) and (15.3),
a A2 B2 and
tan 1
B
A