[Series] Lyla’s Notes on Acoustic Spaces (Vol. 2): Creating a ‘Measurable Sound Field’ from the Inverse Square Law and K2

Introduction

“I’m measuring in an anechoic chamber, but the results vary.” “Some frequency bands are reliable, others are not.” “I haven’t changed the conditions, but the repeatability is poor.”

When consulting on acoustic measurement and evaluation, we sometimes hear these desperate cries. Even if a facility is a fine “anechoic chamber,” whether it truly functions as a suitable measurement environment is an entirely different issue.

This time, we will clarify what a “measurable sound field” is, based on the guiding principles: “Inverse Square Law” and “Environmental Correction.”

A Free Field is Not an “Ideal State”

The term “Free Field” is sometimes misunderstood as an “ideal state with absolutely no reflections, like outer space.” However, in actual measurement practice, a free field is not a theoretical ideal state, but rather a state that “can be confirmed.”

The method used for this confirmation is the Inverse Square Law.

The Inverse Square Law is a “Check Method,” Not a “Theory”

Sound radiated from a point source attenuates in inverse proportion to the square of the distance. “If the distance is doubled, the sound pressure level decreases by about 6 dB.” This is a famous law learned in physics class, but what is crucial in the measurement field is “how far and at which frequencies this relationship holds true.”

• The -6 dB relationship breaks down just by slightly changing the microphone distance.
• Attenuation is disturbed only in specific frequency bands.

In such cases, even if the building is an “anechoic chamber,” the space cannot be called a free field suitable for measurement.

The Concept of “Annex K” that Restricted Anechoic Chamber Design

Here, let’s look back at a little history. The old standard ISO 3745:2003 had “Annex K” established as a design guideline for anechoic chambers.

This Annex specified the conditions for establishing an anechoic chamber in great detail:

• The sound absorption material on walls and ceilings must have a normal incidence sound absorption coefficient of 0.99 or more at the target frequency.
• The length, including the absorption wedges and the air gap behind them, must be 1/4 (λ/4) or more of the target wavelength.

These were rational design guidelines at the time for reliably achieving a free field.

The Reason Why “Ear-Pinging Anechoic Chambers” Were the Norm

Meeting these conditions inevitably required very long and massive glass wool absorption wedges. As a result, many anechoic chambers became spaces where:

• They were so quiet that you felt a sense of discomfort the moment you entered.
• You felt a sense of pressure because the sound was absorbed too much.
• The so-called “ear-ringing” sensation occurred.

At the time, there was a belief that this state was proof of a “high-performance anechoic chamber.”

2012 Revision: A Shift in Evaluation Axis

However, Annex K was removed in the 2012 standard revision. This signifies a major shift in the evaluation axis for anechoic chamber design.

The design up until then was based on a “structure and specification-centric” approach:

• Which materials are used?
• What is the sound absorption coefficient?
• Do the wedge dimensions meet the criteria?

After the revision, the evaluation axis is consolidated into one point: “Does a free field hold true as a result?”

“How it Behaves” Over “How it Was Made”

This change provided great freedom in anechoic chamber design. Designers were no longer bound by sound absorption coefficients or wedge lengths, allowing them to flexibly choose materials and shapes. The key point is that the evaluation is not based on “what materials were used,” but on “how the sound field behaves (i.e., whether the inverse square law holds true).”

The Concept of Environmental Correction

In acoustic power measurements, a concept called “Environmental Correction” is used (e.g., K2 value in ISO 3744). This correction is often understood as a “convenient coefficient for adjusting the value after measurement,” but its meaning differs from a design perspective.

Environmental correction is an indicator that represents “the state of the sound field itself,” showing:

• How much influence from reflection and interference remains.
• The degree of uncertainty in the sound field.

The Correction Value is a “Result,” Not an “Object of Manipulation”

While the environmental correction value is calculated through measurement, it cannot be manipulated afterwards. The arrangement of the absorption structure, the distance to reflective surfaces, and the reflection characteristics for each frequency—the accumulation of these factors appears as the final correction value.

Therefore, in design, the crucial perspective is not “how to subtract the correction,” but “how to create a sound field where the correction is small (i.e., close to a free field).”

What is a “Measurable Sound Field”?

To summarize the discussion so far, a “measurable sound field” is a space that satisfies the following conditions:

1. The Inverse Square Law holds true within the required distance range.
2. Variation across frequency bands is small.
3. The results are repeatable even when measurement conditions are changed.

This is judged not by “the name of the building being an anechoic chamber,” but by “whether the behavior of the sound field can be verified.”

Next Time Preview: The Acoustic Space to Build

Next time: “The Acoustic Space to Build – The Choice of Anechoic Chamber, Soundproof Room, or Anechoic Box.”

We will organize, from Sonora’s perspective, the reasons why “a large anechoic chamber is not the only solution,” and the idea of designing acoustic spaces by scaling (size) according to the object of measurement.

See you in the next notes!

—— Shinkai Laila