(a) The equation of the standing wave is:

y = 4sin(3pt - 6px) - 4sin(3pt + 6px)
Now consider the trig. identity sin(x) - sin(y) = 2sin[(x-y)/2]cos[(x+y)/2].
This gives y = 8sin(-6px)cos(3pt)
The negative sign can come out of the sine function to give:

y = -8cos(3pt)sin(6px)

(b) (i) t = 0

y = -8cos(3p0)sin(6px)
y = -8sin(6px)



(ii) t = T/4

T=2p/w = 2p/3p = 2/3 therefore t = 1/6 and the standing wave is
y = -8cos(3p/6)sin(6px) = 0



(iii) t = 3/15 T

at t = 3T/15 = 3x2/15x3 = 2/15
The standing wave is y = -8cos[3p(2/15)]sin(6px) = -8cos(2p/5)sin(6px) = -2.47sin(6px)



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