Acoustic equivalent for ohm's law plane progressive waves acoustics sound pressure level particle velocity characteristic specific acoustic impedance Z sound units intensity acoustic characteristic impedance dB SPL calculations pascal audio calculations sound units audio engineering

• Formulas and calculation •

Sound pressure p, particle velocity v, specific acoustic impedance of air Z, sound intensity I or J

Acoustics and vibrations

• Acoustic equivalent for Ohm's law •
or ohm's law as equivalent in the acoustics for
plane progressive waves − Specific acoustic impedance

The particle velocity v is not the speed of sound c = velocity of sound.
Unless otherwise stated, the sound pressure is always meant as RMS value.
eff = RMS Enter any two of the following values and click the calculation button.
The missing values will be calculated. One of these values could be the
specific acoustic impedance (characteristic impedance) of air:
Z₀ = 413 N·s/m³ at 20 °C = 68 °F or Z₀ = 410 N·s/m³ at 25 °C = 77 °F.

Sound pressure p N/m² = Pa ≡ V or E voltage

Particle velocity v m/s ≡ I current

Acoustic impedance Z N·s/m³ ≡ R  resistance

Sound intensity J or I W/m² ≡ P power

Fundamentals: Acoustic Laws and Equations
in Analogy (Relationship) to the Electric Laws − Formulary

Formula wheel ♥ Important formulas

Acoustics Sound + noise

In acoustics sound pressure, particle velocity, and acoustic impedance are linear sound
field strength quantities. The sound intensity is a quadratic sound energy strength quantity.

Sound pressure p in pascals is not the same physical quantity as
intensity J or I in watts per square meter.
... and the sound power (acoustic power) does not decrease with
distance r from the sound source - neither with 1 / r nor as 1 / r².

Often the sound pressure as a sound field quantity is mixed incorrect
with the sound intensity as a sound energy quantity. But I ≈ p².

Note: The radiated sound power (sound intensity) is the cause -
and the sound pressure is the effect.
The effect is of particular interest to the sound engineer.
The effect of temperature and the sound power.

Acousticians and sound protectors (noise fighters) need the
sound intensity (acoustic intensity). As a sound designer you
don't need that; look out more for the sound pressure as an
effect to your ears and to the microphones.

Sound pressure and sound power

The well known law V = I × R means accordingly (equivalent) in the acoustics p = v × Z.

Conversion of acoustic values to sound level L in dBSPL
Conversions and Calculations of Sound Quantities and their Levels
Relationships of acoustic quantities associated with acoustic sound waves
How many decibels (dB) is twice (double, half) or three times as loud?
Ohm's Law of the electronics V = I × R

Hearing is directly sensitive to sound pressure (ear drums). In stereo the level differences have
been called "intensity" differences, but sound intensity is a specifically defined quantity and cannot
be sensed by a simple microphone, nor would it be of value in music recordings if it could be.
"Intensity" stereophony is better termed as level difference stereophony, because our
eardrums and microphone diaphragms are moved by the differences of the sound pressure level.

Since our ears do not respond to the particle velocity (sound velocity),
but only on the sound pressure changes, the particle velocity is
irrelevant on the loudness perception.

Acoustic impedance of a medium = Sound pressure / Particle velocity
Characteristic acoustic impedance Z₀ = p / v

Please enter two values, the third will be calculated.

Acoustic impedance Z₀ N·s/m³

Sound pressure p Pa = N/m²

Particle velocity v m/s

Acoustic impedance of air is Z₀ = 413 N·s/m³ at 20 °C.

Acoustic impedance = Density of medium × Speed of sound
Z₀ = ρ × c

Please enter two values, the third will be calculated.

Density of medium ρ kg/m³

Acoustic impedance Z₀ N·s/m³

Speed of sound c m/s

Density of air is ρ = 1.204 kg/m³ at 20 °C.

Medium
Density
ρ in kg/m³ Speed of sound
c in m/s at 20 °C Acoustic impedance
Z₀ in N·s/m³

Air                       1.204              343                413.5

Water       1 000           1 440   1 440 000

Brick       1 700           4 300   7 310 000

Glass quartz       2 200           5 500 12 100 000

Aluminium       2 700           6 100 16 500 000

Steel       7 500           6 000 45 000 000

The decrease of sound with distance

How does the volume (loudness) decrease with distance from a sound source?
How does the sound pressure (voltage) decrease with distance from a sound source?
How does the sound intensity (not the sound power) decrease with distance from a sound source?
The beginners question is quite simple: How does the sound decrease with distance?

For a spherical wave we get:
The sound pressure level (SPL) decreases with doubling of distance by (−)6 dB.
It falls to the 1/2 fold (50%) of the initial value of the sound pressure.
The sound pressure decreases with the ratio 1/r to the distance.

The sound intensity level decreases with doubling of distance also by (−)6 dB.
It falls to the 1/4 fold (25%) of the initial value of the sound intensity.
The sound intensity decreases with the ratio 1/r² to the distance.

The loudness level decreases with doubling of distance also by (−)6 dB.
It falls to the 0.66 fold (66%) of the initial value of the sensed loudness.
The loudness decreases with the ratio 1/(2^0.6r) = 1/1.516 r to the distance.

What is sound? Sound is a pressure fluctuation in the air. It has the character of a wave
motion which is triggered when an air-particle triggers the next. This domino effect is
propagated in air at 343 m / s at 20°C as a longitudinal wave. In liquids and solids the
speed is significantly higher (water: 1440 m/s, steel: 6000 m/s).
Audible sound pressure fluctuations in Pa = pascal are in the range of about 20 µPa =
0 dB (threshold of hearing) up to 150 Pa = 137.5 dB (threshold of pain). The average air
pressure of atmosphere at sea level is 101325 Pa = 1013.25 hPa.
The number of pressure variations (cycles) per second is called "frequency of sound". The
unit of sound frequency is Hertz (Hz). The audible range for humans is between 20 Hz and
20 000 Hz (20 kHz). High frequencies are perceived louder than low frequencies.
Therefore, in measurements of noise, an A weighting filter is often used (human sense of
hearing). When there are very loud or very low frequencies, better use a C-weighted filter.

Sound power and sound pressure.
Correlation between sound energy quantity, and sound field quantity.
A sound source emits sound power and generates a certain sound. That means:
The sound power is the cause and the sound pressure is the effect.
A comparison of the theory of heat makes the connection clear: The head radiated by an
electric heater makes a certain temperature in the room. How high the temperature will be,
depends on room size, type of isolation, the presence of other heat sources and so on.
The power output of the electric heater is always the same, practically independent of the
room in which it is located.
The situation is similar with the sound: The sound that we perceive, or a microphone
perceives, depends on the distance to the sound source and the acoustic characteristics
of the area in which sound waves propagate. In a large, sound-absorbent rooma sound
source sounds much softer than in a small room with bare concrete walls. But the sound
power of the sound source is always the same.

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Medium	Density ρ in kg/m³	Speed of sound c in m/s at 20 °C	Acoustic impedance Z₀ in N·s/m³
Air	1.204	343	413.5
Water	1 000	1 440	1 440 000
Brick	1 700	4 300	7 310 000
Glass quartz	2 200	5 500	12 100 000
Aluminium	2 700	6 100	16 500 000
Steel	7 500	6 000	45 000 000