Tyco 579-769 specifications Speaker Basics, Equation 2-8. The Inverse Square Law

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Speaker Basics

Inverse Square Law

Speakers are essentially “point sources” of sound. Sound radiates outward in all directions,

 

creating a spherical sound pattern. The sound pressure is spread over an increasingly larger

 

surface area as the sound moves away from the source. This causes a drop in loudness per unit

 

area. The drop in SPL is referred to as the “Inverse Square Law,” and originates from the fact that

 

as the diameter of the sound-sphere doubles, the surface area increases by a factor of four. This

 

behavior of outwardly radiating sound causes a drop in SPL of –6 dB per doubling of distance.

 

You can calculate the change in SPL at any distance from a speaker as follows:

D1

 

Δ dBspl = 20 log

 

D2

D1 D2

Equation 2-8. The Inverse Square Law

The figure below illustrates how SPL decreases with distance as you move away from a speaker:

Figure 2-3. dB and Distance Chart

Continued on next page

2-9

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Contents Fire Alarm Audio Applications Guide Page Copyrights and Trademarks Page Table of Contents Emergency Voice/Alarm Communications Systems Glossary of Terms Related Publications Chapter Speech Intelligibility Overview Speech Intelligibility Importance Designing for Topic See Page # Chapter Background InformationEquation 2-2. Ohm’s Law Equation 2-3. Power RelationshipsBasic Audio Math Equation 2-1. The DecibelEquation 2-6. Adding Decibels Equation 2-5. dB and Sound Pressure LevelsRobinson and Dadson Equal Loudness Curves Sound and HearingSpeech Pattern that Illustrates Modulations Nature of SpeechRoom Acoustics Eyring Equation, used when α Sabine Equation, used when αAreas with high ceilings, specify a more directional speaker Equation 2-8. The Inverse Square Law Speaker BasicsEquation 2-9. On-Axis SPL Calculation SPL = Sensitivity + 20 log87dB 6dB/divisionEquation 2-10. Directivity Factor Q for a Conical Source 51º Critical Polar Angle Calculations 104Listener Height = 1.5 Meters Ceiling Coverage Diameter Equation 2-11. Coverage Area CalculationsMinimum Overlap Layout Pattern Selection GuideSPL Variation by Layout Pattern 2x Edge-to-EdgeDistributed Wall Mounted Systems Opposite Speaker WidthWall Mounted Speakers In Meters Room Coverage Width Edge-edge Minimum-Overlap Full-Overlap Chapter Speech Intelligibility Frequency of Speech Contribution to Intelligibility Influences on IntelligibilityNo Noise With Added Noise Degradation of CIS vs. Signal-to-Noise RatioBackground Noise Reverberation Distortion Correlation of CIS and with STI and %ALcons Measures of IntelligibilityALcons STI method with faster measurement times STI-CIS Analyzer Talkbox Practical Measurement of IntelligibilityTools for Predicting Intelligibility Page Chapter Emergency Voice/Alarm Communications Systems Advantages Typical Emergency Voice/Alarm Communications SystemParts of an Emergency Voice/Alarm Communications System Class a and B Speaker Circuit Wiring Chapter Regulatory Issues From Nfpa 72, 2002 Edition AudibilityHigh Background Noise Large Areas Intelligibility Intelligibility Certification Page Chapter Speaker System Design Method Determine the speaker-to-listener distance D2 Speaker Design MethodRecommendations for Maximizing System Intelligibility ITool Office Space Example Applying the MethodsOffice Space Speaker Location Guide Corridor Design Example Corridor SPL Distribution Corridor Speaker Location GuideITool Gymnasium Example 10. Gymnasium Speaker Location Guide 13. Lobby Example 15. Lobby Layout Applying the Methods Conclusion Page Chapter Glossary of Terms Glossary Glossary Page Index IN-2 Page 579-769 Rev. C