Oscillating term

Amplitude

is a function of position x

is a function of position x

Using the following trigonometric identity

we may write y_{res}(x,t) as

Note that the amplitude of a standing wave varies with position. This
is not the case for a sinusoidal traveling wave for which the amplitude is
the same for all positions along the string.

Two waves y_{1}(x,t) and y_{2}(x,t) of the same
amplitude and frequency moving in **opposite directions** on the same string
**interfere** to produce the resultant
wave y_{res}(x,t)