Question

Consider two sinusoidal sine waves traveling along a string, modeled as

*y*_{1}(*x*, *t*) = (0.4 m)sin[(7
m^{−1})*x* − (5 s^{−1})*t*]

and

*y*_{1}(*x*, *t*) = (0.4 m)sin[(7
m^{−1})*x* + (5 s^{−1})*t*].

What is the wave function of the resulting wave? (Hint: Use the trig identity

sin(*u* ± *v*) = sin(*u*) cos(*v*) ±
cos(*u*) sin(*v*).

Use the following as necessary: *x* and *t*.
Assume *x* and *y* are measured in meters and
*t* is measured in seconds. Do not include units in your
answer. Simplify your answer completely.)

*y*(*x*, *t*) =

Answer #1

*y*_{1}(*x*, *t*) = (0.4 m)sin[(7
m^{−1})*x* − (5 s^{−1})*t*]

and

*y*_{2}(*x*, *t*) = (0.4 m)sin[(7
m^{−1})*x* + (5 s^{−1})*t*]

The resulting equation is given as

*y*(*x*, *t*) =
*y*_{1}(*x*, *t*) +
*y*_{2}(*x*, *t*)

*y*(*x*, *t*) = (0.4 m)sin[(7
m^{−1})*x* − (5 s^{−1})*t*] + (0.4
m)sin[(7 m^{−1})*x* + (5
s^{−1})*t*]

*y*(*x*, *t*) = (0.4) (2) Sin(7x)
Cos(5t)
(Since Sin(A + B) + Sin(A - B) = 2 SinA CosB)

*y*(*x*, *t*) = (0.8) Sin(7x)
Cos(5t)

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