Two loudspeakers are mounted on a rack, one h = 3.48 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. 8.00 m The loudspeakers are driven by the same tone generator and vibrate in phase at 520 Hz. It is possible to create a condition of destructive interference at Point O by changing one or both of the path lengths (r, and r,) 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.)
Two loudspeakers are mounted on a rack, one h = 3.48 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. 8.00 m The loudspeakers are driven by the same tone generator and vibrate in phase at 520 Hz. It is possible to create a condition of destructive interference at Point O by changing one or both of the path lengths (r, and r,) 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.)
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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![### Problem: Interference of Sound Waves
#### Diagram Explanation:
The diagram shows two loudspeakers mounted on a rack, one positioned at height \( h = 3.48 \, \text{m} \) above the other. The speakers emit sound waves that travel to a point \( O \), where a microphone is situated. Point \( O \) is located 8.00 meters horizontally to the right of the speakers' midpoint. The distances \( r_1 \) and \( r_2 \) represent the path lengths from each speaker to the microphone at point \( O \).
#### Given:
- Frequency of sound: \( 520 \, \text{Hz} \)
- Speed of sound in air: \( 343 \, \text{m/s} \)
- Initial vertical separation between the speakers: \( h = 3.48 \, \text{m} \)
- Horizontal distance to microphone: \( 8.00 \, \text{m} \)
#### Objective:
Determine the smallest vertical distance \( \Delta h \) by which you need to raise the upper speaker to achieve destructive interference at point \( O \).
#### Concept:
Destructive interference occurs when the path difference between two waves is a half-integer multiple of the wavelength (\( (n + \frac{1}{2})\lambda \)).
1. Calculate the wavelength (\(\lambda\)) using the formula:
\[
\lambda = \frac{\text{Speed of sound}}{\text{Frequency}} = \frac{343 \, \text{m/s}}{520 \, \text{Hz}}
\]
2. Consider the path difference criteria for destructive interference.
3. Solve for \( \Delta h \) based on the condition for destructive interference, adjusting \( r_1 \) and \( r_2 \).
Use this setup to analyze the conditions necessary to achieve the desired interference pattern.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F459d8b63-efb7-453b-af0e-0b7134cd3e8e%2Ff85dad18-1ac7-47b2-ab65-7158ea1a149b%2F681o5oe_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem: Interference of Sound Waves
#### Diagram Explanation:
The diagram shows two loudspeakers mounted on a rack, one positioned at height \( h = 3.48 \, \text{m} \) above the other. The speakers emit sound waves that travel to a point \( O \), where a microphone is situated. Point \( O \) is located 8.00 meters horizontally to the right of the speakers' midpoint. The distances \( r_1 \) and \( r_2 \) represent the path lengths from each speaker to the microphone at point \( O \).
#### Given:
- Frequency of sound: \( 520 \, \text{Hz} \)
- Speed of sound in air: \( 343 \, \text{m/s} \)
- Initial vertical separation between the speakers: \( h = 3.48 \, \text{m} \)
- Horizontal distance to microphone: \( 8.00 \, \text{m} \)
#### Objective:
Determine the smallest vertical distance \( \Delta h \) by which you need to raise the upper speaker to achieve destructive interference at point \( O \).
#### Concept:
Destructive interference occurs when the path difference between two waves is a half-integer multiple of the wavelength (\( (n + \frac{1}{2})\lambda \)).
1. Calculate the wavelength (\(\lambda\)) using the formula:
\[
\lambda = \frac{\text{Speed of sound}}{\text{Frequency}} = \frac{343 \, \text{m/s}}{520 \, \text{Hz}}
\]
2. Consider the path difference criteria for destructive interference.
3. Solve for \( \Delta h \) based on the condition for destructive interference, adjusting \( r_1 \) and \( r_2 \).
Use this setup to analyze the conditions necessary to achieve the desired interference pattern.
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