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.

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