Sound intensity level

Sound intensity level is a sound “loudness” level measured in decibels. It is measured with a sound level meter (decibel meter).

Fig. 1. Example sound level meter

Sound pressure level can be determined from the following formula.

Sound pressure level formula:

where:

L_p – sound pressure level,
p₁ – sound pressure generated by the source in micropascals,
p₂ – common sound pressure level reference point, the threshold of hearing for a human ear, 20 μP.

Sound level formula:

where:

L_I – sound pressure level,
I – sound intensity [W/m²],
I₀ – reference sound intensity 10^-12 [W/m²].

Fig. 2. Example sound characteristics

1 - silence
2 - sound

Other units used instead of micropascals include microbars [μb] and dynes/cm².

The sound intensity level is 0 dB if the sound pressure p₁ is equal p₂, i.e. at the threshold of hearing.

The human ear have a logarithmic response to sound pressure, rather than a linear one. It can hear sounds in the frequency range of 16 Hz to 20,000 Hz.

However, no all sounds from this range can be heard properly. The pain threshold is approx. 110 dB to 140 dB.

The table shows common ambient sounds and the corresponding sound intensity level.

Sound source	Acoustic pressure (Pa)	Sound level (dB)
Absolute threshold of hearing	0.00002	0
Normal threshold of hearing		10
Rustling of leaves	0.0002	20
Recording studio		30
Silent apartment	0.002	40
Private office		50
Conversation	0.02	60
Traffic	0.2	80
Truck	2	100
Riveting press	20	120
Pain threshold		135
Helicopter	200	140
Jet engine	2000	160
Sound pressure at the distance of 3 m from the detonated 25 kg TNT	100000	194

Sound level is an A-weighted sound intensity level, i.e. modified by the properties of the human ear, which can hear properly in the entire frequency range at high pressure levels and may vary (depending on the frequency) at lower sound pressure levels.

Fig. 3. A-weighting curve for sound level

1 - sound pressure level (dB)
2 - frequency (Hz)

Phon is a unit of loudness level. The loudness of any sound expressed in phons corresponds to the sound intensity (in decibels) at 1 kHz - with the loudness equal to the loudness of the sound.

Fig. 4. Thresholds of hearing

1 - loudness level in phons [phon]
2 - threshold of hearing
3 - sound pressure level (dB)
4 - frequency (Hz)

As shown in the diagram (Fig. 4), the thresholds of hearing are slightly different at the range of frequencies audible to the human ear. The loudness curves show a relative decrease in ear sensitivity at lower tones (low frequencies).