Visual Guide to Critical Distance for Sound

Understanding how distance affects the transmission and intelligibility of sound is important to hearing care professionals.  Understanding critical distance for sound helps the hearing professional counsel patients more effectively.

For some, attempting to apply formulae and actually make measurements is more than they want.  Therefore, this post is an attempt to have a picture (or more than one) be worth a thousand words.  Let’s start with Figure 1.

Figure 1. Direct sound from the speaker/talker/signal diminishes in level as a function of distance (modified from Lenard Audio Institute, education.lenardaudiocom).
Figure 1. Direct sound from the speaker/talker/signal diminishes in level as a function of distance (modified from Lenard Audio Institute, education.lenardaudiocom).

 

From our studies on basic acoustics, it is known that the direct sound from the sound source diminishes in level as a function of the distance (inverse square law) – roughly falling at 6 dB for each doubling of distance.  Indoors, where listening occurs most frequently, any reflected sound (from walls, ceilings, floors, other room surfaces) adds to the direct sound such that sound pressure no longer falls smoothly with distance.  On the other hand, reverberation constantly spreads throughout the enclosure (room).

At close distances from a sound source, the direct sound is still stronger than any returning reflected sound.  In a room, the direct sound falls at roughly 6dB for each doubling of distance, but it won’t be exactly 6 dB because of strong reflections from the walls, ceilings, floors, and other room objects/surfaces.  Four or five dB reduction with distance doubling might be more realistic.  Regardless, as the distance from the source increases, the sound pressure of the direct sound continues to fall until it reaches the same intensity as that of the reverberant sound.  This point is identified as the “Critical Distance.”

Stated another way, “Critical Distance” is the distance from the sound source where the direct and reverberant sound energies become equal (Figure 2).

Figure 2. The critical distance depends on the ratio (R) of the direct and reverberant sound. When the critical distance is close to the sound source, it indicates that the reverberation in the room is high. If the critical distance is distant from the sound source, the room has good absorbance. In a 100% absorbent room, the critical distance would be at the walls. The turquoise lines associated with the Small R and Large R indicate the sound level of the reverberation.
Figure 2. The critical distance depends on the ratio (R) of the direct and reverberant sound. When the critical distance is close to the sound source, it indicates that the reverberation in the room is high. If the critical distance is distant from the sound source, the room has good absorbance. In a 100% absorbent room, the critical distance would be at the walls. The turquoise lines associated with the Small R and Large R indicate the sound level of the reverberation.

 

Every enclosed space has a critical distance value.  When working closer to the sound source than the critical distance, this is said to be working in the “near (or direct) field.”  When working farther away from the critical distance, this is said to be working in the “far (or reverberant) field.”

Take Away

  • The more reverberant the room, the closer the Critical Distance
  • The more absorbent the room, the further the Critical Distance
  • Near field, or direct field, is inside the Critical Distance
  • Far field, or reverberant field, is outside the Critical Distance

About Wayne Staab

Dr. Wayne Staab is an internationally recognized authority on hearing aids. As President of Dr. Wayne J. Staab and Associates, he is engaged in consulting, research, development, manufacturing, education, and marketing projects related to hearing. Interests away from business include fishing, hunting, hiking, mountain biking, golf, travel, tennis, softball, lecturing, sporting clays, 4-wheeling, archery, swimming, guitar, computers, and photography. Among other pursuits.

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