Sound Level – Decibels, Intensity, and Distance

Loud sound – How does the load and sound level change as you move away? Clearly, the sound gets quieter, but how much quieter is it? Let’s join DASM to find the answer in the article below

Sound Level, Sound Intensity

The sound intensity level is calculated in W/m², and the comparison between two sounds with intensities I and Io is calculated in decibels using the formula:

Decibel level = 10 log (I/Io)

For example, using the threshold of hearing with an intensity of Io = 10⁻¹² W/m², we can calculate the decibel level of a sound with an intensity of 10⁻⁶ W/m².

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Decibel level = 10 log (10⁻⁶ / 10⁻¹²) = 10 log (10⁶) = 60 dB, which represents the intensity at the ears of two people having a normal conversation.

However, in the case of people with a hearing threshold of 100 dB, using the following formula, we can calculate the intensity of the sound they hear:

Decibel level = 10 log (I / 10⁻¹²) = 100

Therefore:

10¹⁰ = I / 10⁻¹², and thus I = 10¹⁰ × 10⁻¹² = 10⁻² W/m².

However, the intensity of sound decreases in proportion to the inverse square of the distance.

Intensity at distance d₁ / Intensity at distance d

So, what happens when you are farther away, such as at the other end of the room? The sound level is clearly less here (to simplify, we will ignore reflections from the walls in the room).

In other words, if I am 2 meters away from the source and you are 20 meters away, you would experience an intensity of 10⁻² × (2² / 20²) = 10⁻⁴ W/m² (one percent of the sound intensity at my ears), and a decibel level of
10 log (10⁻⁴ / 10⁻¹²) = 80 dB – still loud enough to be considered a loud stereo system.

Doubling the distance between the listener and the sound source will reduce the decibel level by more than 6 dB.

This can be calculated as follows: The intensity is reduced to 1/4 of its initial value, and thus the change in decibels is:

10 log (1/4) = -6.02 dB.

The negative sign means the decibel level decreases. Reducing the distance would lead to an increase in the decibel level, producing a positive sign for the change in decibels.

The graph below illustrates how both the intensity and decibel level vary with distance from the sound source, with the decibel level at 80 dB at 20 meters.

As explained, sound level and intensity decrease with distance according to the inverse square law. The decibel level decreases as the distance between the sound source and the listener increases. Although the sound diminishes with distance, this reduction is not linear but follows a logarithmic scale. The calculation of decibel levels and sound intensity relative to distance can be applied in various scenarios, from outdoor sound to indoor environments, helping us better understand how sound spreads and affects the surrounding area.