Question

Two waves on one string are described by the wave functions

*y*_{1} = 2.5 cos(4.5*x* −
1.3*t*)

*y*_{2} = 4.5 sin(5.5*x* − 1.5*t*)

where *x* and *y* are in centimeters and
*t* is in seconds. Find the superposition of the waves
*y*_{1} + *y*_{2} at the following
points. (Remember that the arguments of the trigonometric functions
are in radians.)

(a) *x* = 1.00, *t* = 1.00

cm

(b) *x* = 1.00, *t* = 0.500

cm

(c) *x* = 0.500, *t* = 0

cm

Answer #1

y_{1} = 2.5 cos(4.5x − 1.3t)

On putting the above values

y_{1} = 2.5Cos3.2 = -2.4957

y_{2} = 4.5 sin(5.5x − 1.5t)

y_{2} = 4.5Sin(4) = -3.406

Now

y_{1} + y_{2} = -2.4957 +(-3.406) = -5.9013

(b) x = 1 , t = 0.5

y_{1} = 2.5 cos(4.5x − 1.3t)

On putting the above values

y_{1} = 2.5Cos3.85 = -1.8985

y_{2} = 4.5 sin(5.5x − 1.5t)

y_{2} = 4.5Sin(4.75) = -4.497

Now

y_{1} + y_{2} = -1.8985 +(-4.497) = -6.3955

(c) x = 0.5 , t = 0

y_{1} = 2.5 cos(4.5x − 1.3t)

On putting the above values

y_{1} = 2.5Cos2.25 = -1.5704

y_{2} = 4.5 sin(5.5x − 1.5t)

y_{2} = 4.5Sin(2.75) = 1.7175

Now

y_{1} + y_{2} = 1.7175 +(-1.5704) = 0.1471

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