Sound Power

Sound Power $(P)$

$P=\frac{A{p}^2}{\rho c}\cdot cos\theta$

• $A$ is the area of the surface;
• $\rho$ is the mass density;
• $c$ is the sound velocity;
• $\theta$ is the angle between the direction of propagation of the sound and the normal to the surface.
• $p$ is the sound pressure.

In air, $\rho =1.2kg/m^3$ and $c=343m/s$

Sound Pressure Level SPL $L_p$ - $(dB)$

Sound pressure $p$ $(N/m^2)$ or $(Pa)$

$L_p=20\log \frac{p}{p_0}$ where $p$ is sound pressure in pascals $(Pa)$ and $p_0=20\text{micro}Pa$ accordance with ISO 1683. $p_0$ comes from lowest sound pressure that human can hear at $3,000-4,000Hz$

Sound Level $(L)$ vs Distance $(r)$

$L_1-L_2=|20\cdot \log \frac{r1}{r2}|$ Sound level drop by 6 dB per double the distance.

Sound intensity $(I)$

$P=AI$ where

• A stands for the area;
• I stands for the sound intensity.

Sound energy density $(\omega )$

$P=Ac\omega$ where

• c stands for the speed of sound;
• w stands for the sound energy density.

Calculator

https://mehlau.net/audio/spl/

function doCalc() {
	var efficiency = eval(formSPL.efficiency.value * 1)  // SPL (1W/1m)
	var dBPower = eval(10 * (Math.log(formSPL.power.value) / Math.log(10)));  // Amp Power Watt
	var dBDistance = eval(-20 * ((Math.log(formSPL.distance.value) / Math.log(10)))); // m
	var dBPlacement = eval(formSPL.placement.value);
	var dBResult = eval(efficiency + dBPower + dBDistance + dBPlacement * 1);  // dB
	dBResult = round(dBResult, 1);
	formSPL.result.value = dBResult;
}
 
<option value="0">Away from walls</option>
<option selected value="3">Close to wall (60-120cm)</option>
<option value="6">In corner (45-60cm)</option>

SPL

SPL

SPL @ 1W/1m

How many decibels (dB) are doubling a sound

 $\times 2$ the sound intensity is +3 dB.
 $\times 2$ the sound pressure is +6 dB.
 $\times 2$ the loudness feeling is about +10 dB.

 $\times 2$ the power (Watt) is +3 dB. 10 dB = 10-fold  $\times 2$ the Voltage $(V)$ or Current $(I)$ is +6 dB. 20 dB = 10-fold

ref. Damping of sound level

The human perception of loudness

Pressure Level Change	Volume Loudness	Voltage / Sound pressure	Acoustic Power / Sound Intensity
+40 dB	16	100	10000
+30 dB	8	31.6	1000
+20 dB	4	10	100
+10 dB	2 double	3.16 = $\sqrt{10}$	10
+6 dB	1.52 times	2 double	4
+3 dB	1.23 times	1.414 times = √2	2 double
±0 dB	**- - - 1.0 - - - **	- - - 1.0 - - -	- - - 1.0 - - -
−3 dB	0.816 times	0.707 times	0.5 half
−6 dB	0.660 times	0.5 half	0.25
−10 dB	0.5 half	0.316	0.1
−20 dB	0.25	0.1	0.01
−30 dB	0.125	0.0316	0.001
−40 dB	0.0625	0.01	0.0001
Log. size	Psycho size	Field size	Energy size
dB change	Loudness multiplier	Amplitude multiplier	Power multiplier

From Genelec

https://www.genelec.com/correct-monitors

Sound Basics

Sound is ultimately pressure which exists in a sequence of waves which propagates through compressible media such as air or water. Sound travels approximately 344 m/s (1130 ft/s). It takes 3 ms for sound to travel 1 metre (3,3 ft).

In free-field conditions (no walls, floor, or ceiling) the sound volume drops 6 dB when the distance doubles.

Distance	Sound Level	Volume Drop
1 m	100 dB	0 dB
2 m	94 dB	-6 dB
4 m	88 dB	-12 dB

Sound level increases by 3 dB when the amplifier power doubles.

Amp Power	Sound Level	Volume Increase
100 W	85 dB	0 dB
200 W	88 dB	+3 dB
400 W	91 dB	+6 dB

The industry standard reference sound pressure level (SPL) for cinema and TV sound production work is between 82 and 85 dB at the listening position.

Frequency Spectrum

The frequency spectrum of an electrical signal is, by definition of Collins online dictionary, “the distribution of the amplitudes and phases of each frequency component against frequency”. The audible frequency spectrum covers 10 octaves (up to 40 Hz, 80, 160, 320, 640, 1’280, 2’560, 5’120, 10’240, 20’480 Hz) which can conveniently divide the spectrum as follows.

Subsonic bass frequencies	below 16 Hz	Not audible for humans.
Very low frequencies	16 – 40 Hz 40 – 80 Hz	Lowest audible octave for humans. Music low frequencies, kick drums, bass instruments
Low frequencies	80 – 160 Hz 160 – 320 Hz	Low register of a grand piano. Middle C of a piano.
Midrange frequencies	320 – 1,280 Hz	Music midrange frequencies
Upper midrange frequencies	1,280 – 2,560 Hz 2,560 – 5,120 Hz	Low-order harmonics of most instruments. The ear is the most sensitive in this range.
High frequencies	5,120 – 10,240 Hz	Brightness and harmonics
Extremely high frequencies	10,240 – 20,480 Hz	Highest harmonics. Inaudible to humans above 20 kHz