What Determines the Point of Minimum Loudness in Speaker Interference?

Click For Summary
SUMMARY

The point of minimum loudness in speaker interference occurs due to destructive interference, which is determined by the distances from the listener to each speaker. In this case, with speakers S1 and S2 separated by 2.78 meters and emitting sound at a frequency of 587 Hz, the wavelength is calculated to be 0.584 meters. The first distance at which Hillary hears minimum loudness corresponds to the condition where the path difference between the sound waves from the two speakers is equal to half a wavelength (n=±1). This principle is critical for understanding sound wave interactions in acoustics.

PREREQUISITES
  • Understanding of wave properties, specifically wavelength and frequency.
  • Knowledge of sound interference, including constructive and destructive interference.
  • Familiarity with basic trigonometry to analyze distances and angles in wave propagation.
  • Concept of path difference in wave mechanics.
NEXT STEPS
  • Study the principles of sound wave interference in detail.
  • Learn how to calculate path differences for multiple sound sources.
  • Explore the effects of speaker placement on sound quality and loudness.
  • Investigate the relationship between frequency, wavelength, and sound perception.
USEFUL FOR

Acoustics students, audio engineers, and anyone involved in sound design or speaker placement optimization will benefit from this discussion.

Student3.41
Messages
70
Reaction score
0

Homework Statement



Hillary stands directly in front of speaker S1 and walks straight away (down on the page) from S1 as shown in the diagram.

What is the first distance (measured from S1) at which she will hear minimum loudness? Speed of sound is 343 m/s and the frequency of the sound is 587 Hz. The speakers are 2.78 m apart

Can someone explain what the significance of the speaker separation is in problems also??

Homework Equations





The Attempt at a Solution



Solved for Wave length = 0.584m, I then figured minimum loudness would be where constructive interference fisrt meets n=+/-1. So what do i do...
 

Attachments

  • Speakers_4.jpg
    Speakers_4.jpg
    2 KB · Views: 469
Physics news on Phys.org
Noone?, again.. I figured outthe beat question.
 
Minimum loudness will correspond to destructive interference, not constructive interference.

Compare Hillary's distance to S1, with Hillary's distance to S2. What must be true about those distances in order to have destructive interference? (Your textbook or class lecture notes should have something to say about this.)
 

Similar threads

Audio interference of sound waves from two speakers
  • · Replies 19 ·
Replies
19
Views
5K
Sound Interference Problem -- Observer moving between two speakers
  • · Replies 3 ·
Replies
3
Views
4K
What is the Maximum Wavelength for Constructive Interference of Sound Waves?
  • · Replies 3 ·
Replies
3
Views
3K
Sound Wave Interference and Finding the Path Differences with Diagrams
  • · Replies 20 ·
Replies
20
Views
5K
Sound wave Interference from Two Speakers
  • · Replies 3 ·
Replies
3
Views
4K
Constructive interference with sound -- word problem
  • · Replies 15 ·
Replies
15
Views
3K
Destructive vs Constructive interference
  • · Replies 2 ·
Replies
2
Views
4K
Destructive interference and constructive interference
  • · Replies 3 ·
Replies
3
Views
3K
Question on destructive and constructive interference
  • · Replies 6 ·
Replies
6
Views
3K
How Far Must Point P Be from Speaker A for Constructive Interference at 400 Hz?
  • · Replies 1 ·
Replies
1
Views
1K