Acoustic equivalent for ohm's law - plane progressive waves acoustics sound pressure particle velocity units acoustic impedance Z sound intensity characteristic specific acoustic impedance audio engineering sound recording - sengpielaudio
 
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● 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.
Formula   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 or the 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 Sound
Equations in Analogy (Relationship) to the
Ohm's Law. Formulary and Audio Equations
 Formula wheel ♥  Important formulas
Acoustics   Sound + noise
Formula wheel acoustics
The Formula Wheel of Acoustics (Audio)
 
In acoustics and audio engineering sound pressure, air particle velocity, and acoustic impedance are linear sound field strength quantities. The sound intensity is a quadratic sound energy strength quantity.
 
Specific acoustic impedance Z0 = ρ · c = p / v
ρ = density of air and c = speed of sound
 
 
Sound pressure p in pascals (newtons per square meter) 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.
Die sound energy quantity is proportional to the sound field quantity squared.

 
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 sound pressure.
 

 
Acousticians and sound protectors (noise fighters) need the sound intensity (acoustic intensity). As a sound designer you don't need that energy quantity.
Look out more for the sound pressure that makes an effect to the eardrums of our hearing and to the diaphragms of microphones.
 

Sound pressure and Sound power − Effect and Cause

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
Temperature Dependence of Physical Entities

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 air particle velocity (sound velocity), but only to 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

In 1970, the pressure reference level of 0 dB ≡ 1 µPa was chosen by the US Navy for their underwater work for sound in water.
For an identical source intensity in water and air, the sound pressure generated in water will be about 60 times greater than in air.

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.
The sound pressure falls falls to the 1/2 times (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.
The intensity falls to the 1/4 times (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.
The loudness falls to the 2/3 times (ca. 63%) of the initial value of the sensed loudness.
The loudness decreases with the ratio 1/(20.66r) = 1/1.581 r to the distance.
There was a discussion: 2−0.6r is not the same thing as 1/(20.6)r which shows that
the equation is wrong. But how is it right?

http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Science/2009_December_27#Sound_pressure.2C_sound_intensity.2C_sound_loudness.2C_and_decay_with_distance

 
The sound level depends on the distance between the sound source and the place of measurement, possibly one ear of a subject.
The sound pressure level Lp in dB without the given distance r to the sound source is really useless. Unfortunately this error (unknown distance) is quite often.
 

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 heat 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 room a 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.
Look at: "Sound pressure and Sound power − Effect and Cause"
http://www.sengpielaudio.com/SoundPressureAndSoundPower.pdf

 
The sensitivity (transfer factor) in mV / Pa shows clearly that microphones change sound pressure (Pa) to audio voltage (mV).
Energy and power play no role for these microphone transducers.
Also our eardrums are only moved by the sound pressure.
Sound pressure as a sound field quantity cannot be the same as acoustic intensity as a sound energy quantity.
 

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