Answer:
Step-by-step explanation:
To solve this problem, we can use the following equations for the addition of two sinusoidal waves:
y1 = A1 sin(ωt + φ1)
y2 = A2 sin(ωt + φ2)
where A1 and A2 are the amplitudes of the waves, ω is the angular frequency, t is time, and φ1 and φ2 are the initial phase angles.
(a) To find the resultant amplitude of the two waves, we can use the following equation:
Ar = √(A1^2 + A2^2 + 2A1A2cos(φ2 - φ1))
where Ar is the resultant amplitude.
Substituting the given values, we get:
Ar = √((3.0 × 10^(-6))^2 + (4.0 × 10^(-6))^2 + 2(3.0 × 10^(-6))(4.0 × 10^(-6))cos(150° - 60°))
Ar ≈ 5.03 × 10^(-6) m
Therefore, the resultant amplitude is approximately 5.03 × 10^(-6) m.
(b) To find the resultant's initial phase angle, we can use the following equation:
tan(φr) = (A1sin(φ1) + A2sin(φ2))/(A1cos(φ1) + A2cos(φ2))
where φr is the initial phase angle of the resultant wave.
Substituting the given values, we get:
tan(φr) = (3.0 × 10^(-6)sin(60°) + 4.0 × 10^(-6)sin(150°))/(3.0 × 10^(-6)cos(60°) + 4.0 × 10^(-6)cos(150°))
φr ≈ 142.85°
Therefore, the resultant's initial phase angle is approximately 142.85°.
(c) The circle of reference and the time graph for the sine waves can be drawn as follows:
Sine Waves
The blue and red arrows represent the maximum displacement of the waves. The black arrow represents the displacement of the resultant wave. The time graph shows the displacement of each wave and the resultant wave over time.