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Engineeringtoolbox: Abatement and Distance from Source
| It is often stated that sound pressure level = SPL, sound intensity level = SIL and sound power level = SWL are not comparable. SPL is measured in pascals = N/m2, sound intensity is energy measured in W/m2, and sound power is measured in watts? Do you really know that sound power level is equal to sound pressure level and intensity level at a distance of r = 0.2821 m from the source at full sphere propagation? 1 watt of sound power = 120 dB Sound intensity at r = 0.2821 m: Pac = 1 watt / (4 × π × r2) = 1 watt, that means (4π × r2) = 1 and r = √(1/4π). 10 × log (1/10−12) = 120 dB Sound pressure level SPL at 0.2821 m = SWL − (20 × log (r) − 11) = 120 − (20 × log (0.2821) − 11) = 120 dB So how can they not be comparable? |
Free Field sound propagation. Sound power is neither room |
| Important: The sound level should not be confused with sound power level! The dB values in sound pressure levels are always tied to the distance to the sound source, however, the dB values in sound power level have really no relation to the distance from the sound source. |
| To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
r = √(Q / 4 · π)
| Geometry |
Directivity factor Q |
Equal level at r |
r dB |
| No surface near sound source; able to radiate acoustical energy in all directions; full sphere |
1 | √(1/4π) = 0.2821 m | 11 |
| Sound source close to a flat surface; able to radiate acoustical energy to half of a sphere (hemi) |
2 | √(1/2π) = 0.3989 m | 8 |
| Close to two adjacent flat surfaces perpendicular to each other; able to radiate to one fourth of a sphere |
4 | √(1/π) = 0.5642 m | 5 |
| At a corner; able to radiate acoustical energy to one eighth of a sphere |
8 | √(2/π) = 0.7979 m | 2 |
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| Full sphere Q = 1 Half sphere Q = 2 Quarter sphere Q = 4 Eighth sphere Q = 8 |
| For the practically occurring solid angle, we get the following relationships between the sound power and sound pressure level For Q = 1 is LW = Lp + [20 log r/m + 11] dB For Q = 2 is LW = Lp + [20 log r/m + 8] dB For Q = 4 is LW = Lp + [20 log r/m + 5] dB For Q = 8 is LW = Lp + [20 log r/m + 2] dB Lp = medium soundpressure level au the envelope (hemispherical surface) and for the most frequent case of radiation hemisphere r = 1m: LW = Lp + 8 dB |
| Spherical Free Field Sound Propagation, Q = 1 |
| The sound pressure in a spherical distance from a source with a known sound power can be expressed as: |
 (1)where p = sound pressure in Pa = N/m2 ρ = density of air in kg/m3: 1.2041 kg/m3 at 20°C c = speed of sound in m/s: 343.22 m/s at 20°C Pac = sound power in W π = 3.14159 r = distance from source in m Q = directivity factor (spherical = 1, half spherical = 2) |
directivity index - directivity factor - directivity coefficient
| For a spherical sound propagation (Q = 1) at a distance of r = √(1/4π) = 0.2821 m the decibel value of the sound pressure level is equal to the sound power level. |
| Hemispherical Sound Propagation, Q = 2 |
| The directivity coefficient Q depends on several parameters − the position and direction of the source, the room or the surrounding area, etc. The sound pressure level Lp can be expressed logarithmic as: Lp = 20 log (p/p0) = 20 log ((Q ρ c Pac/(4 π r2))1/2/p0) = 20 log (1/r (Q ρ c Pac/(4 π))1/2/p0) (2) where Lp = sound pressure level in dB p0 = 2 × 10-5 - reference sound pressure in Pa Note: That for every doubling of the distance from the noise source, the sound pressure level Lp, will be reduced by 6 decibels. |
| For a spherical sound propagation (Q = 2) at a distance of r = √(1/2π) = 0.3989 m the decibel value of the sound pressure level is equal to the sound power level. |
| For point-like sources of sound, we get a spherical surface A. Depending on the arrangement in space spherical segments are to consider: Solid sphere - sound source anywhere in the room, Q = 1 Hemisphere - sound source on the ground Q = 2 Quarter-sphere - sound source on the wall, Q = 4 Eighth sphere - sound source in the corner, Q = 8 Q = directivity factor and the area A = (4 · π · r2) / Q |
| Sound Pressure Level Calculator |
| Consider a source of sound and imagine a sphere with radius r, centered on the source. The sound source outputs a total power P, continuously. The sound intensity I is the same everywhere on this surface of a thought sphere, by definition. The intensity I is defined as the power P per unit area A. The surface area of the sphere is A = 4 π r2, so the sound intensity passing through each square meter of surface is, by definition: I = P / 4 π r2. We see that sound intensity is inversely proportional to the square of the distance away from the source (1/r2): I2 / I1 = r12 / r22. But sound intensity is proportional to the square of the sound pressure, I ~ p2, so we can write: p2 / p 1 = r1 / r2. The sound pressure p changes with 1 / r of the distance. So, if we double the distance, we reduce the sound pressure by a ratio of 2 and the sound intensity by a ratio of 4: in other words, we reduce the sound level by 6 dB. If we increase r by a ratio of 10, we decrease the level by 20 dB. |
W. T. W. CORY: "Relationship between Sound pressure and Sound Power Levels"
| Power is like all energy quantities primarily a calculated value. |
| "Sound power" and "sound pressure" are two distinct and commonly confused characteristics of sound.
They have a cause and effect relationship. Sound power is the acoustical energy emitted by the sound source, and is an absolute value. It is not affected by the environment.
Sound power levels are connected to the sound source and are independent of distance. Sound power levels are indicated in decibels.
Lw = 10×log (W / W0) where: The reference power is 10−12 watts (W), which is the lowest sound persons of excellent hearing can discern. Sound power is measured as the total sound power emitted by a source in all directions in watts (joules per second). Since sound measuring instruments respond to sound pressure the "decibel" is generally associated with sound pressure level (SPL). Sound pressure levels quantify in decibels the intensity of given sound sources. Sound pressure levels vary substantially with distance from the source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors. Sound pressure levels are indicated in decibels. Sound pressure level (SPL) is Lp = 20×log (p / p0), where: The reference sound pressure is p0 = 2×10−5 Pa = 20 µPa. Sound pressure is a pressure disturbance in the air whose intensity is influenced not only by the strength of the source, but also by the surroundings and the distance from the source to the receiver. Sound pressure is what our ears hear and what sound pressure level meters (SPL meters) measure. |
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