Two Waves on One String Are Described by the Wave Functions

Two waves in one string are described by the wave functions:

y1 = (3.0cm)cos(4.0x-1.6t)

y2 = (4.0cm)sin(5.0x-2.0t)

where y and x are in centimeters and t is inseconds. Find the superposition of the wavesy1+y2 at the points (a) x=1.00, t=1.00; (b)x=1.00, t=.500; and (c) x= 0.500, t=0.

Answer

given
two waves are described as
y1 = (3.0cm)cos(4.0x-1.6t)&  y2 = (4.0cm)sin(5.0x-2.0t)
a)
At x = 1cm & t = 1.0s
we have
y =y1+y2
=(3.0cm)cos(4.0*1-1.6*1) + (4.0cm)sin(5.0*1-2.0*1)
=3cos(2.4rad)+4sin(3rad)
=-2.212 + 0.5645
=-1.647cm
b)
At x=1.00, t=0.500
we have
y =y1+y2             =(3.0cm)cos(4.0*1-1.6*0.5)+ (4.0cm)sin(5.0*1-2.0*0.5)
=-2.995 +(- 3.027)
=-6.022cm
c)
At x= 0.500, t=0
we have
y =y1+y2             =(3.0cm)cos(4.0*0.5-1.6*0)+ (4.0cm)sin(5.0*0.5-2.0*0)
=- 1.248 + 2.394
=1.146cm

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