Acoustic Quantities LMS Test.Lab Rev 12A Copyright LMS International 2012
Table of Contents Chapter 1 Acoustic quantities... 5 Section 1.1 Sound power (P)... 5 Section 1.2 Sound pressure... 5 Section 1.3 Sound (Acoustic) intensity... 6 Section 1.4 Free field... 7 Section 1.5 Particle velocity... 7 Section 1.6 Acoustic impedance (Z)... 8 Chapter 2 Reference conditions... 9 Section 2.1 Sound power level Lw... 9 Section 2.2 Particle velocity level Lv... 9 Section 2.3 Sound (Acoustic) intensity level LI... 10 Section 2.4 Sound pressure level LP... 10 Chapter 3 Octave bands... 11 Section 3.1 Octave filter midband and edge frequencies... 11 Section 3.2 Octave filter shapes... 14 Section 3.2.1 Octave Filtering Options in Test.Lab... 15 Chapter 4 Acoustic weighting... 17 Section 4.1 Frequency weighting... 17 Rev 12A 3
Chapter 1 Acoustic quantities Chapter 1 Acoustic quantities In This Chapter Sound power (P)... 5 Sound pressure... 5 Sound (Acoustic) intensity... 6 Free field... 7 Particle velocity... 7 Acoustic impedance (Z)... 8 Section 1.1 Sound power (P) The amount of noise emitted from a source depends on the sound power of that source. The sound power is a basic characteristic of a noise source, providing an absolute parameter that can be used for comparison. This differs from the sound pressure levels it gives rise to, which depend on a number of external factors. The total sound power PI of a source surrounded by N measurement surfaces is given by: The power of a sound source is expressed in Joules per second, or Watts. The sound power can also be represented by the letter W. Section 1.2 Sound pressure The effect of the sound power emanating from a source is the level of sound pressure. Sound pressure is what the ear detects as noise, the level of which depends to a great extent on the acoustic environment and the distance from the source. The sound pressure is defined as the difference between the actual and ambient pressure. This is a scalar quantity that can be derived from measured sound pressure spectra or autopower spectra either at one specific frequency (spectral line), or integrated over a certain frequency band. Sound pressure measurements can be obtained at each measurement point, and are independent of the measurement direction (X,Y, or Z). The units are Pascal (Pa) or N/m2. Rev 12A 5
Chapter 1 Acoustic quantities Section 1.3 Sound (Acoustic) intensity An important quantity to be derived from the sound power is sound intensity. The sound intensity of a sound wave describes the direction and net flow of acoustic energy through an area. Sound intensity is a vector, orientated in 3D-space with the fundamental units of W/m2, (power transmitted per unit area). The area is represented as a vector in 3D space with a length equal to the amount of geometrical area, and a direction perpendicular to the measurement surface. As such, the vector product (Ii.Si) represents the flow of acoustic energy in a direction perpendicular to a surface. This is the usual direction in which intensity is measured. If the acoustic intensity vector lies within the surface itself, the transmitted sound power equals zero. Intensity is also the time-averaged rate of energy flow per unit area. As such, if the energy is flowing back and forth resulting in zero net energy flow then there will be zero intensity. Normal sound intensity This is the component of the sound intensity vector normal to the measurement surface. 6 LMS Test.Lab Acoustic Quantities
Chapter 1 Acoustic quantities Section 1.4 Free field This term refers to an idealized situation where the sound flows directly out from the source and both pressure and intensi ty levels drop with increasing distance from the source according to the inverse square law. Diffuse field In a diffuse field the sound is reflected many times such that the net intensity can be zero. Section 1.5 Particle velocity Pressure variations give rise to movements of the air particles. It is the product of pressure and particle velocity that results in the intensity. In a medium with mean flow therefore where: p= sound pressure (Pa) = particle velocity (m/s) The particle velocity of a medium is defined as the average velocity of a volume element of that medium. This volume element must be large enough to contain millions of molecules so that it may be thought of as a continuous fluid, yet small enough so that acoustic variables such as pressure, density and velocity may be considered to be constant throughout the volume element. Rev 12A 7
Chapter 1 Acoustic quantities Equation 2-4 can be used to compute the particle velocity, once the acoustic intensity and the sound pressure have been measured. Particle velocity is a vector in 3D-space expressed in units of (m/s). In a diffuse field the pressure and velocity phase vary at random giving rise to a net intensity of zero. Under certain circumstances (i.e. plane progressive waves in a free field), the particle velocity can also be calculated from the pressure and the impedance of the medium (rc). where: pe= effective sound pressure (Pa) = mass density of the medium (kg/m3) c= velocity of sound in the medium (m/s) By combining equations 2-4 and 2-5 it can be seen that in a free field a relationship exists enabling the acoustic intensity to be determined from the effective pressure of a plane wave. Section 1.6 Acoustic impedance (Z) This is defined as the product of the mass density of a medium and the velocity of sound in that medium. where: = mass density (kg/m3) c = velocity of sound in the medium (m/s) 8 LMS Test.Lab Acoustic Quantities
Chapter 2 Reference conditions Chapter 2 Reference conditions In This Chapter Sound power level Lw... 9 Particle velocity level Lv... 9 Sound (Acoustic) intensity level LI... 10 Sound pressure level LP... 10 It is a common practise to define standards for acoustic intensity, pressure, etc... at an air temperature of 20 C and a standard atmospheric pressure of 1023 hpa (1 bar). Under these conditions the density of air the velocity of sound in air c the acoustic impedance = 343 (m/s) = 1.21 (kg/m3) = 415 rayls (kg/m2s) db scale Since the range of pressure levels that can be detected is large and the ear responds logarithmically to a stimulus, it is practical to express acoustic parameters as a logarithmic ratio of a measured value to a reference value. Hence the use of the decibel scales for which the reference values for intensity, pressure and power are defined below. Section 2.1 Sound power level Lw This is defined as the logarithmic measure of the absolute (unsigned) value of the sound power generated by a source. The reference sound power is P0 = 10-12 (W) Section 2.2 Particle velocity level Lv This is defined as the logarithmic measure of the particle velocity. Rev 12A 9
Chapter 2 Reference conditions The reference particle velocity is v0 = 50 10-9 (m/s) Section 2.3 Sound (Acoustic) intensity level LI This is the logarithmic measure of the absolute value of the intensity vector. The commonly used reference standard intensity for airborne sounds is Io= 10-12 (W/m2) Normal acoustic intensity level (LI) This is the logarithmic measure of the absolute value of the normal intensity vector. Section 2.4 Sound pressure level LP This is defined as p is the rms value of the acoustic pressure (in Pa) The above reference values for intensity and power correspond to an effective rms reference pressure of po = 0.00002 (Pa) = 20 mpa This sound pressure level of 20 mpa is known as the standardized normal hearing threshold and represents the quietest sound at 1000Hz that can be heard by the average person. 10 LMS Test.Lab Acoustic Quantities
Chapter 3 Octave bands Chapter 3 Octave bands In This Chapter Octave filter midband and edge frequencies... 11 Octave filter shapes... 14 Section 3.1 Octave filter midband and edge frequencies There are two accepted methods to determine the midband frequencies of the octave bands: the base-2 method: subsequent center frequencies have a ratio of 2 1/b with 1/b the bandwidth designator (e.g. b=3 for 1/3 octave band). Edge frequencies are derived from the center frequency by multiplying or dividing with 2 1/(2b). The reference frequency is f r=1000 Hz. Center frequencies are given by: f cn=f r*2 n/b for b odd f cn=f r*2 (2n+1)/(2b) for b even the base-10 method: subsequent center frequencies have a ratio of (10 3/10 ) 1/b with 1/b the bandwidth designator (e.g. b=3 for 1/3 octave band). Edge frequencies are derived from the center frequency by multiplying or dividing with (10 3/10 ) 1/(2b). The reference frequency is 1000 Hz. f cn=f r*(10 3/10 ) n/b for b odd Rev 12A 11
Chapter 3 Octave bands f cn =f r*(10 3/10 ) (2n+1)/(2b) for b even Note: Current IEC 61260:1995 and ANSI S1.11-2004 standards accept both base-10 and base-2, but recommend base-10. Some standards (e.g. ISO 266-1997) are based on base-10 but mention that base-2 may be used as an acceptable approximation because the differences are small (10 3/10 = 1.995262). Note: Apart from the exact midband frequencies as mentioned above, the designation of the band will be expressed in nominal midband frequencies (typically rounded numbers, also specified in the standards for full and 1/3 octaves) and not with the exact midband frequencies (according to e.g. ISO 266-1997 and ANSI S1.6-1984(R2006)). For a list of normalized midband frequencies, see the table further. Note: With base-10 system, midband frequencies of 1/3 octave band will include e.g. 10, 100, 1000, 10000 (ratio of 10). Other midband frequencies digits will also repeat themselves apart from the location of the decimal points. For the base-2 system, the 100 Hz (nominal) third octave band will have a midband frequency of 99.2126 Hz while the 10000 Hz (nominal) third octave band will have a midband frequency of 10079.37 Hz. 12 LMS Test.Lab Acoustic Quantities
Chapter 3 Octave bands Note on even fractional octaves: Different formulas are used to locate center frequencies for b=odd (1, 1/3 octave) and b=even (1/2; 1/6, 1/12, 1/24). This means that the reference frequency (1000 Hz) is a center frequency for b=odd and an edge frequency for b=uneven (e.g. 1/2, 1/6, 1/12 octave). The purpose of this is to be able to split an octave band in smaller fractions, covering the same edge frequencies as the original one: e.g. the 1000 octave band can be split in 2 ½ - octave band with 1000 lying just at the edge of both. The definition of the even fractional octaves changed in the period 1995-1997. Until that period, the center frequencies of even fractional octaves such as 1/2, 1/6, 1/12 and 1/24 octaves were based on the known octave center frequencies (e.g.: 250Hz, 500Hz, 1000Hz, etc). This approach has the disadvantage that the sum of two ½ octaves does not add up to an octave level. In the above mentioned period 1995-1997, ISO 226 removed the definition of even fractional octaves from the standard and mentions only 1/1 and 1/3 octaves. The IEC standard on the calculation of time based fractional octaves, adapted the definition to the alternative approach to keep the filter cut-off frequencies as references, hence allowing even fractional octaves to add up to the next level of octaves. Consequently, the known octave center frequencies are no longer valid center frequencies. Data from other sources, CADA-X data and older Test.Lab data (before 8B) might still be measured according to this older convention. Rev 12A 13
Chapter 3 Octave bands Section 3.2 Octave filter shapes When implemented in the time domain as digital band-pass filter banks on sampled data, the relative attenuation of the filters is never perfect (no attenuation between the edges and full attenuation outside the edges). The current IEC 61260:1995 and ANSI S1.11-2004 standards give an upper and a lower limit for the relative attenuation, depending on the Class of analyzer. These limits allow a shape of the filter response which attenuates before the edge frequencies and with a finite slope beyond the edge frequencies. When converting data to octave band in the frequency domain, it is much easier (and common practice) to implement a (nearly) ideal filter (i.e. a square filter shape): only energy on the frequency lines within the octave band will be summed. However, in order to match as closely as possible data processed with time-domain filters with data processed with FFT, it is also possible to use filter shapes with a smoother shape (ANSI Emulation). This requires more processing, as for each octave band, (weighted) integration over more frequency lines will be done. 14 LMS Test.Lab Acoustic Quantities
Chapter 3 Octave bands Section 3.2.1 Octave Filtering Options in Test.Lab Section 3.2.1.1 Time-based For time-based octave filtering, it is possible to select 3 methods in Test.Lab: ANSI-IEC Class1 base 10: the recommended setting as it complies with the latest IEC and ANSI standard and uses base 10 as recommended by the standard ANSI base 2: for compatibility with previous (before 8A) releases (ANSI method used in Signature throughput processing) IEC base 2: for compatibility with previous releases (before 8A) (IEC method used in Signature throughput processing) This choice influences host-based octave calculations performed with the ANSI-IEC Octave Filtering add-in (e.g. Signature throughput processing or RTO in parallel with Fixed sampling acquisition). Front-end based octave filtering (available in the RTO workbook) will always use an ANSI-IEC Class1 base 2 filter implementation. Section 3.2.1.2 FFT-based For FFT-based octave filtering (e.g. done in Octave display of narrowband data, in Signature Fixed sampling, by the Octave function in the Data calculator etc ), it is possible to select between: Ideal base 10: the recommended setting (only method before 8A) Ideal base 2: for compatibility with e.g. CADA-X data ANSI Emulation base 10: if similarity with time-domain filters is important (before 8A, only possible in Signature Processing with the ANSI Emulation option set in the setup) ANSI Emulation base 2: for compatibility with e.g. CADA-X data Rev 12A 15
Chapter 4 Acoustic weighting Chapter 4 Acoustic weighting In This Chapter Frequency weighting... 17 Section 4.1 Frequency weighting The human ear has nonlinear, frequency dependent characteristics, which means that the sensation of loudness cannot be perfectly described by the sound pressure level or its spectrum. To derive an experienced loudness level from the sound pressure signal, the frequency spectrum of the sound pressure signal is multiplied by a frequency weighting function. These weighting functions are based on experimentally determined equal loudness contours which express the loudness sensation as a function of sound pressure level and frequency. A number of equal loudness contours are shown in Figure 2-1. The loudness level is expressed in Phons. 1 khz-tones are used as the reference, which means that for a 1000 Hz tone, the Phon value corresponds to the db sound pressure level. Figure 2-1 Equal loudness perception contours A, B and C - weighting for acoustic signals. A-weighting modifies the frequency response such that it follows approximately the equal loudness curve of 40 phons and is applied to signals with a sound pressure level of 40dB. The A-weighted sound level has been shown to correlate extremely well with subjective responses. The B and C-weighting follow more or less the 70 and 100 phon contours respectively. These contours can be seen in Figure 2-2. The resulting value is then denoted by LA, LB,... with unit dba, dbb... Rev 12A 17
Chapter 4 Acoustic weighting Table 2.2 (overleaf) shows the relative response attenuations or amplifications of the 3 types of filters. In between the listed normal frequencies, these filter spectra are linearly interpolated on a log-log scale. Figure 2-2 shows the same information in a graphical form. 18 LMS Test.Lab Acoustic Quantities
Chapter 4 Acoustic weighting Rev 12A 19
A Index Acoustic impedance (Z) 8 Acoustic quantities 5 Acoustic weighting 23 F FFT-based 21 Free field 7 Frequency weighting 23 O Octave bands 15 Octave filter midband and edge frequencies 15 Octave filter shapes 20 Octave Filtering Options in Test.Lab 21 P Particle velocity 7 Particle velocity level Lv 12 R Reference conditions 11 S Sound (Acoustic) intensity 6 Sound (Acoustic) intensity level LI 12 Sound power (P) 5 Sound power level Lw 11 Sound pressure 5 Sound pressure level LP 13 T Time-based 21 Rev 12A 21