Sound pressure level

Sound measurements
Sound pressure p
Sound pressure level (SPL)
Particle velocity v
Particle velocity level (SVL)
(Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power Pac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Surface S
Acoustic impedance Z
Speed of sound c v • d • e

Sound pressure is defined as the difference between the average local pressure of the medium outside of the sound wave in which it is traveling through (at a given point and a given time) and the pressure found within the sound wave itself within that same medium. A square of this difference (i.e. a square of the deviation from the equilibrium pressure) is usually averaged over time and/or space, and a square root of such average is taken to obtain a root mean square (RMS) value. For example, 1 Pa RMS sound pressure (94 dBSPL) in atmospheric air implies that the actual pressure in the sound wave oscillates between (1 atm Pa) and (1 atm Pa), that is between 101323.6 and 101326.4 Pa. Such a tiny (relative to atmospheric) variation in air pressure at an audio frequency will be perceived as quite a deafening sound, and can cause hearing damage, according to the table below.

As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale. The sound pressure level (SPL) or L_p is defined as

where p is the root-mean-square sound pressure and p_ref is a reference sound pressure. Commonly used reference sound pressures, defined in the standard ANSI S1.1-1994, are 20 µPa in air and 1 µPa in water. Without a specified reference sound pressure, a value expressed in decibels cannot represent a sound pressure level.

Since the human ear does not have a flat spectral response, sound pressures are often frequency weighted so that the measured level will match perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.

Examples of sound pressure and sound pressure levels

Source of sound	RMS sound pressure	sound pressure level
	Pa	dB re 20 µPa
Theoretical limit for undistorted sound at 1 atmosphere environmental pressure	101,325	~194.094
Limit [Atmospheric pressure records] Min & Max western Pacific Ocean 1979 (Typhoon Tip) & Agata, U.S.S.R. 1968	87,000 - 108,400	192.8 - 194.7
1883 Krakatoa eruption	~20,000	~180 at 100 miles
Stun grenades	6324.55 - 20,000	170 - 180
rocket launch equipment acoustic tests	~3556	~165
~threshold of pain	100.237	134
~ hearing damage during short-term effect	20	120
jet engine, 100 m distant	6.32455 – 200.000	110 – 140
jackhammer, 1 m distant / discotheque	2	approx. 100
~hearing damage from long-term exposure	0.63246	85
traffic noise on major road, 10 m distant	0.20000 – 0.63246	80 – 90
moving automobile, 10 m distant	0.02000 – 0.20000	60 – 80
~TV set – typical home level, 1 m distant	0.02000	60
normal talking, 1 m distant	0.00200 – 0.02000	40 – 60
very calm room	0.00020 – 0.00063	20–30
quiet rustling leaves, calm human breathing	0.00006	10
auditory threshold at 2 kHz – undamaged human ears	0.00002	0

Equipment for dealing with sound

Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers.