1-10 Standing waves

Oscillating term

Amplitude
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 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 y_res(x,t)