Question

The wave functions

y₁(x, t) = (0.150 m)sin(3.00x − 1.50t)

and

y₂(x, t) = (0.250 m)cos(6.00x − 3.00t)

describe two waves superimposed on a string, with x and y in meters and t in seconds. What is the displacement y of the resultant wave at the following. (Include the sign of the value in your answers.)

(a)    

x = 0.700 m

and

t = 0

m

(b)    

x = 1.15 m

and

t = 1.15 s

m

(c)    

x = 1.55 m

and

t = 4.80 s

m

Answer 1

Put your calculator in radian mode

(a)

y = (0.150 m)sin(3.00x − 1.50t) + (0.250 m)cos(6.00x − 3.00t)

y = (0.150 m)sin(3.00*0.7 − 1.50*0) + (0.250 m)cos(6.00*0.7 − 3.00*0)

y = 0.12948 - 0.122565

y = 0.0069147 m

_______________

(b)

y = (0.150 m)sin(3.00*1.15 − 1.50*1.15) + (0.250 m)cos(6.00*1.15 − 3.00*1.15)

y = 0.14822 - 0.238

y = - 0.08998 m

_________________

(c)

y = (0.150 m)sin(3.00*1.55 − 1.50*4.8) + (0.250 m)cos(6.00*1.55 − 3.00*4.8)

y = - 0.08365 + 0.09449

y = 0.0108 m