Question

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

y₁(x, t) = (0.4 m)sin[(7 m⁻¹)x − (5 s⁻¹)t]

and

y₁(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

y₁(x, t) = (0.4 m)sin[(7 m⁻¹)x − (5 s⁻¹)t]

and

y₂(x, t) = (0.4 m)sin[(7 m⁻¹)x + (5 s⁻¹)t]

The resulting equation is given as

y(x, t) = y₁(x, t) + y₂(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)