Two in-phase wave sources S_1 and S_2, are located at (0 m, 0 m) and (8 m, 0 m). They vibrate...


Two in-phase wave sources {eq}S_1 {/eq} and {eq}S_2 {/eq}, are located at ({eq}0 m, 0 m {/eq}) and ({eq}8 m, 0 m {/eq}). They vibrate identically, each obeying the equation {eq}Y_{source} = (2 cm) sin (24\pi t) {/eq}. What is the amplitude of the resultant wave at point {eq}P (0 m, 15 m) {/eq} assuming the amplitude of each wave does not decrease as they travel. The speed of the wave is {eq}v = 1.92 m/s {/eq}.

Interference of the fields of two coherent in-phase oscillation sources.

The superposition of the fields of two sources of harmonic in-phase oscillations creates an interference picture of variable intensity. This intensity depends on the difference in the distances of a given point from two sources.

Answer and Explanation:

The equation for the waves coming from two sources are as follows

{eq}A_1(r,t)=2cm*sin(24\pi*(t-|r-r_1|/v)) {/eq}

{eq}A_2(r,t)= 2cm*sin(24\pi*(t-|r-r_2|/v)) {/eq}

{eq}r=(x,y)-\text{field point vector}, r_1=(0m,0m) -\text{position vector of the first sourse}, r_2=(8m,0m) - \text{position vector of the second source} {/eq}

The amplitude A of the resultant wave at point P(0m,15m)

{eq}A=|A_1(P,t)-A_2(P,t)|=4cm*|cos(12\pi/v*(|P-r_2|-|P-r_1|))|=4cm|cos(12\pi/1.92*2)|=0.03cm {/eq}

Learn more about this topic:

Constructive and Destructive Interference

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 8 / Lesson 16

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