Inverse Square Law: What is it?

Conference rooms bring their fair share of challenges, from poor acoustics to bad connections. While there are many ways to improve your conference experience, one approach that often gets overlooked involves microphone placement and the laws of physics. To better understand the importance of distance to and between microphones, the inverse square law can be a useful concept to know. 

In this guide, we discuss the basics of the inverse square law and how it applies to audio and acoustics.

What is the Inverse Square Law?

The inverse square law is a scientific principle that says the strength of a force, like gravity or light, decreases in proportion to the square of the distance from its source. This means that if you double the distance between two objects, the force between them becomes four times weaker.

In simple terms, the inverse square law states that any energy or force will have a drastic dropoff in strength as it travels further away from the point source. Any source which spreads out in all directions without getting lost obeys the inverse square law. 

This “source” can be applied to the following energies and forces:

  • Sound

  • Gravitation

  • Electrostatics

  • Light

  • Radiation

Examples of Inverse Square Law

The inverse square law can be commonly found in real world situations. Some examples of inverse square law involving different types of forces include:

  • Light: Say you’re driving down a dark highway, and your headlights are on. The light rays from the headlights disperse as they travel. So, the further away the light rays get from the headlights, the more spread out they are. Therefore, the strength of the light rays weaken and shallow out. 

  • Gravity: If you've ever thrown a ball to someone far away, you might have noticed that you need to throw it harder to make it reach them. This is because the force of gravity pulling the ball down to the ground gets weaker as the ball moves farther away from the Earth's surface.

  • Sound: When attempting to record a sound with a microphone, it becomes more difficult to get a loud recording the farther your are from the source. The intensity of the sound, or force, becomes weaker the farther you are from it. In these cases you’ll need to compensate for the distance by increasing the volume or sensitivity of the microphone.

Let’s use light as an example. 

How Does the Inverse Square Law Apply to Sound?

Sound is a form of energy that adheres to the inverse square law. When you’re optimizing a conference room for your business, it’s helpful to have a general understanding of how sound travels and reverberates.

In the realm of acoustics, the inverse square law states that the intensity of sound decreases by approximately 6 dB for each doubling of distance from the sound source. On the other hand, the opposite is true when you move closer to the source.

Let’s say you have a YVC-1000. You connect a microphone to it that’s 1 foot away from your mouth. When you move 2 feet away from the microphone, the sound will decrease by 6 dB. If you double that distance to 4 feet, the sound will drop another 6 dB, resulting in a 12 dB loss from the original level. The diagram to the left should diagram explaining inverse square law.give you a better visualization of how the inverse square law works with acoustics.

Microphone placement is one of the most vital aspects to consider when setting up your ideal conference room. If you’re sitting too far away from the microphone, it’ll pick up more room reverb, making your voice sound muddy and intelligible. For best audio capture, it’s recommended to have a dedicated microphone for each person in your meeting. In this case, the microphones can capture each voice clearly and directly, providing a much better conferencing experience.

Inverse Square Law Formula

The formula for the inverse square law is as follows:

Force (or Intensity) = Constant / Distance^2

In other words, force (or intensity) is inversely proportional to the square of the distance from its source. The constant variable in this formula represents the strength of the force being measured, and will vary depending on the type (e.g. light, gravity, etc…)

Let’s take a look at how to calculate the inverse square law for sound intensity.

Inverse Square Law Calculation for Sound

As mentioned earlier, the inverse square law specifies that the intensity of sound weakens by 6 dB for each doubling of distance from the sound source. However, this explanation is under the context that you’re in a free field – a place where there are no reflective surfaces. Unfortunately, this isn’t the case with most conference rooms, so 6 dB should be viewed more like an approximation.

Sound intensity is defined as power over area. If you want to calculate the sound intensity at any distance from the source, there’s a formula you can use: inverse square law formula.

Here’s what each symbol represents:

  • I = Intensity of sound

  • P = Power of the source

  • r = Distance between the source and the point of interest

The diagram to the left illustrates how sound spreads out and weakens the further away it gets from the source:

Overall, if you take anything away from the inverse square law regarding acoustics, remember that greater distance = lower sound level.

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Learn more about the behavior of sound:

Understanding reverberation
What is speech derverberation?
Sound waves explained
Pink noise vs white noise vs brown nosie
What is DSP?
What is acoustic echo cancellation?