Two loudspeakers are mounted on a rack, one h = 2.74 m above the other. Exactly 8.00 meters to the right of the midpoint, a microphone rests at point O. Point O is equally distant from each loudspeaker. The loudspeakers are driven by the same tone generator and vibrate in phase at 390 Hz.It is possible to create a condition of destructive interference at Point O by changing one or both of the path lengths (r1 and r2) between speaker and microphone. Suppose that this is done by raising the upper speaker while leaving the lower speaker in place. What is the smallest vertical distance (in m) that you would need to raise the upper speaker by, in order to create destructive interference at Point O? (The speed of sound waves in air is 343 m/s.) ### Diagram Explanation: Acoustic Wave InterferenceIn the diagram above, we see a visual representation of an acoustic wave interference setup, which is typically used to understand the principles of wave physics, particularly sound waves.#### Components of the Diagram:1. **Sound Sources**: Two sound sources are depicted on the left side. Each source is represented by a small circular icon with an outward-facing triangular shape, indicating the direction of the sound waves being emitted. 2. **Distances and Path Lengths**: - The vertical distance between the two sound sources is labeled as \( h \). - The horizontal distance from the line connecting the sound sources to the observation point \( O \) is given as \( 8.00 \) meters. - The distances from each sound source to the observation point \( O \) are labeled as \( r_1 \) and \( r_2 \).3. **Sound Paths**: The sound waves from each source travel to the observation point \( O \). These paths are illustrated with straight lines: - The upper path is labeled as \( r_1 \). - The lower path is labeled as \( r_2 \).Understanding this setup is crucial for studying how sound waves interact, specifically how constructive and destructive interference occurs. This can lead to patterns of sound intensity at different points in space, which can be predicted using the principles of wave superposition.This diagram is used in educational contexts to explain concepts such as phase difference, path difference, and interference patterns in the study of wave mechanics and acoustics.

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Two loudspeakers are mounted on a rack, one h = 2.74 m above the other. Exactly 8.00 meters to the right of the midpoint, a microphone rests at point O. Point O is equally distant from each loudspeaker.

The loudspeakers are driven by the same tone generator and vibrate in phase at 390 Hz.

It is possible to create a condition of destructive interference at Point O by changing one or both of the path lengths (r₁ and r₂) between speaker and microphone. Suppose that this is done by raising the upper speaker while leaving the lower speaker in place. What is the smallest vertical distance (in m) that you would need to raise the upper speaker by, in order to create destructive interference at Point O? (The speed of sound waves in air is 343 m/s.)

### Diagram Explanation: Acoustic Wave Interference

In the diagram above, we see a visual representation of an acoustic wave interference setup, which is typically used to understand the principles of wave physics, particularly sound waves.

#### Components of the Diagram:
1. **Sound Sources**: Two sound sources are depicted on the left side. Each source is represented by a small circular icon with an outward-facing triangular shape, indicating the direction of the sound waves being emitted.

2. **Distances and Path Lengths**:
- The vertical distance between the two sound sources is labeled as \( h \).
- The horizontal distance from the line connecting the sound sources to the observation point \( O \) is given as \( 8.00 \) meters.
- The distances from each sound source to the observation point \( O \) are labeled as \( r_1 \) and \( r_2 \).

3. **Sound Paths**: The sound waves from each source travel to the observation point \( O \). These paths are illustrated with straight lines:
- The upper path is labeled as \( r_1 \).
- The lower path is labeled as \( r_2 \).

Understanding this setup is crucial for studying how sound waves interact, specifically how constructive and destructive interference occurs. This can lead to patterns of sound intensity at different points in space, which can be predicted using the principles of wave superposition.

This diagram is used in educational contexts to explain concepts such as phase difference, path difference, and interference patterns in the study of wave mechanics and acoustics.

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