Consider two sinusoidal waves traveling along a string, modeled as y1(x, t) = (0.4 m)sin[(3 m−1)x + (2 s−1)t] and y2(x, t) = (0.8 m)sin[(6 m−1)x − (5 s−1)t]. What is the vertical displacement (in m) of the resultant wave formed by the interference of the two waves at the position x = 0.9 m at time t = 0.4 s? (Indicate the direction with the sign of your answer.)

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Rau7star Rau7star · Answer 1 · 2020-06-08T02:57:15+02:00

Answer:

y(x,t)=-0.395m

Explanation:

The wave function modeling waves are:

[tex]y_1(x,t)[/tex]= (0.4 m)sin[(3 [tex]m^-^1[/tex])x + (2 [tex]s^-^1[/tex])t]

[tex]y_2(x,t)[/tex]=(0.8 m)sin[(6 [tex]m^-^1[/tex])x − (5 [tex]s^-^1[/tex])t]

The principle of superposition can be defined as the resultant of [tex]y_1[/tex] and [tex]y_2[/tex] is equal to their algebraic sum

[tex]y(x,t)=y_1(x,t)+y_2(x,t)[/tex]

y(x,t)= (0.4 m)sin[(3 [tex]m^-^1[/tex])x + (2 [tex]s^-^1[/tex])t] + (0.8 m)sin[(6 [tex]m^-^1[/tex])x − (5 [tex]s^-^1[/tex])t]

Substitute 0.9m for x and 0.4s for t as required

y(x,t)= (0.4 )sin[(3 [tex]m^-^1[/tex])(0.9) + (2 [tex]s^-^1[/tex])(0.4)] + (0.8 m)sin[(6 [tex]m^-^1[/tex])(0.9)− (5 [tex]s^-^1[/tex])(0.4)]

y(x,t)= -0.14 - 0.255

y(x,t)=-0.395m

ConcepcionPetillo ConcepcionPetillo · Answer 2 · 2022-04-01T09:28:53+02:00

The vertical displacement of the resultant wave formed by the interference of the two waves is -0.395m

Two sinusoidal waves are given such that:

y₁(x, t) = (0.4 m)sin[(3 m⁻¹)x + (2s⁻¹)t] and

y₂(x, t) = (0.8 m)sin[(6 m⁻¹)x − (5s⁻¹)t]

The superposition of the two waves gives the outcome of the interference at x = 0.9 m and t = 0.4 s.

y(x,t) = y₁(x, t) + y₂(x, t)

y(0.9,0.4) = y₁(0.9, 0.4) + y₂(0.9, 0.4)

y(0.9,0.4) = (0.4 m)sin[(3 m⁻¹)0.9 + (2s⁻¹)0.4] + (0.8 m)sin[(6 m⁻¹)0.9 − (5s⁻¹)0.4]

y(0.9,0.4) = -0.395m

Learn more about interference:

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