Sound intensity and intensity level

Sound intensity describes how much sound power passes through a given area. The area is taken normal to, or perpendicular to, the direction in which the sound travels.

For sound distributed uniformly over an area $$A$$, the intensity is $$I=P/A$$, where $$P$$ is the sound power passing through that area. Intensity is measured in watts per square metre, $$\mathrm{W,m^{-2}}$$.

Sound intensity level

Sound intensities can span a very large range. Sound intensity level expresses an intensity relative to a reference intensity on a logarithmic scale, measured in decibels ($$\mathrm{dB}$$):

Here, $$I$$ is the sound intensity and $$I_0=1.0\times10^{-12},\mathrm{W,m^{-2}}$$ is the reference intensity, conventionally taken as the threshold of hearing. The ratio $$I/I_0$$ compares the intensity with this reference.

When $$I=I_0$$, the ratio is $$1$$ and its logarithm is zero, so the intensity level is $$0,\mathrm{dB}$$. Zero decibels does not mean zero intensity: it means the intensity equals the reference intensity.

Comparing intensity levels

For two sounds with intensities $$I_1$$ and $$I_2$$ and corresponding levels $$L_1$$ and $$L_2$$, the level difference is:

A tenfold increase in intensity therefore raises the level by $$10,\mathrm{dB}$$. A doubling of intensity raises it by approximately $$3,\mathrm{dB}$$. The same level change always corresponds to the same intensity ratio, not the same difference in intensity.

A logarithmic scale is useful because human perception responds to relative changes in intensity over a very large range. Intensity level does not, however, fully determine perceived loudness: loudness also depends on the sound’s frequency.

Equal-loudness curves

Two tones can have different frequencies and different sound intensity levels, yet be perceived as equally loud. This is because hearing sensitivity varies with frequency: some frequencies need a higher intensity level than others to produce the same perceived loudness.

An equal-loudness curve shows the sound intensity level needed at each frequency for tones to be perceived as equally loud. Frequency is plotted on the horizontal axis and sound intensity level on the vertical axis.

Reading an equal-loudness curve

Every point on a single curve represents the same perceived loudness. The points generally do not have the same sound intensity level. Where the curve is lower, less intensity is needed to produce that loudness, so hearing is more sensitive at that frequency. Where the curve is higher, a greater intensity level is needed.

Different equal-loudness curves represent different perceived loudnesses. A higher curve represents tones judged louder than those on a lower curve.

Producing an equal-loudness curve

A listener compares a tone with a reference tone and adjusts its level until the two are judged equally loud. This is repeated with tones at different frequencies, using the same reference tone. Plotting the matched intensity levels against frequency gives an equal-loudness curve.

Sound-level measurement and A-weighting

A sound level meter uses a microphone to detect variations in air pressure caused by sound. It processes the microphone’s signal and displays a sound level in decibels (dB).

A decibel reading expresses a level on a logarithmic scale relative to a reference. The reading must also be interpreted with its frequency weighting in mind: different weightings give different emphasis to sounds at different frequencies.

A-weighting

Human hearing is more sensitive to some frequencies than to others. A-weighting accounts for this by reducing the contribution of frequencies to which hearing is less sensitive before the meter displays the level. An A-weighted reading is expressed in dBA.

A dBA reading is therefore not simply the same unweighted reading written in a different unit: the meter has processed the sound differently. Two sounds with the same unweighted level can have different A-weighted levels if their frequency content differs. A-weighting is useful for assessing sound levels in relation to hearing sensitivity, but a dBA reading does not give an exact measure of perceived loudness in every situation.