1-10 Standing waves

 

Formula

 

Oscillating term
Amplitude
is a function of position x

 Using the following trigonometric identity

 

we may write yres(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 y1(x,t) and y2(x,t) of the same amplitude and frequency moving in opposite directions on the same string interfere to produce the resultant wave yres(x,t)