Measuring Sound Intensity and Loudness

Humans and animals sense a very wide range of sound amplitude, or loudness - from the very quiet to the extremely loud. It is known that human hearing is not equally sensitive to all sound frequencies and that loudness is very subjective: we don’t all hear the same in response to sound. So how do we measure loudness in an impartial way?

Sound Intensity

To understand loudness, it is useful to start with a more fundamental property of sound: intensity. Sound intensity is the rate at which energy is being carried by a sound wave through a given area. It has the unit of Watts per square meter (W/m²).

Figure 1 shows that sound intensity decreases inversely as the square of the distance. For example, when the distance of the source is doubled, the energy is spread out spherically, over four times the area. Two intensities are related according to the rule:

Sound Intensity Rule: The ratio of two intensities equals the square of their inverse distance ratio (Fig1).

Definition of Sound Level

Humans are able to detect sound intensity as low as the threshold 10‾¹² W/m² and as high as an upper limit of 1.0 W/m², a figure above which we experience pain or damage to hearing. This enormous range of hearing for the human ear is, in fact, sensitivity best represented by a logarithmic scale.

A sound level scale may be derived that compares the intensity of sound, I W/m², with a reference value selected as the threshold of sound, Io W/m²:

Sound Level (dB): L = 10 log (I / Io)

The basic sound level scale is called the Bel, but because the values obtained are too large in the normal range of sound levels, the Decibel is commonly used (1dB = 0.1 Bel).

Worked Examples

A high sound level of 120 dB is regarded as the threshold of pain for the average listener. What is the corresponding intensity? Substituting 120 into the above sound level formula, we get 120 = 10 log (I / 10‾¹²). Then simplifying and taking the antilog yields the answer, I = 1.0 W/m².

If a listener is exposed to this sound level of 120 dB at a distance of 10 m from the source, to what value would the sound level fall if they moved a further 10 m away? Using the intensity ratio formula (Fig 1) and the above answer for intensity, we get I / 1.0 = (10/20)², from which I = 0.25 W/m². This value of intensity is then substituted into the sound level formula: L= 10 log (0.25/10‾¹²), which yields the result L = 114 dB

Sound Level Meter

The Decibel meter is modeled on the human ear, which perceives sound loudness according to a logarithmic response. Also called a "sound level meter" or "dB Meter", it is designed to accurately and objectively measure the sound or noise that one can hear. This places a real value on something as subjective as loudness, which is affected by human perception. The meter may also be used to study how sound pressure changes with distance from the sound source.

Summary

The fundamental property of sound is sound intensity. When compared to a reference value for the threshold of hearing, a logarithmic loudness scale may be derived, called the decibel scale. A sound level meter is based on the decibel scale, but it cannot measure the subjective loudness experienced by a human, only the objective sound pressure levels in the surroundings.

The reader may be interested in more details on this topic or to learn about the sound recording and production.

Fig 1. Calculating Sound Intensity

Sound Level Meter

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