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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