Phase and Group Velocity
y(x,t)={2ym cos [(?k/2)x -(??/2)t]} x sin[(k1+ k2)x/2 -(?1+ ?2)t/2]
y(x,t) = y`m sin( kx - ?t) result is a travelling wave at the average frequency and wave number
?= (?1+ ?2)/2 k =(k1+ k2)/2
new amplitude depends on x and t : y`m ={2ym cos [(?k/2)x -(??/2)t]}
‘carrier’ wave moves at phase velocity vp= ?/k
amplitude modulation moves at group velocity vg= ??/?k