Measurement of Sound Pressure and Sound Pressure Level

Magnitude of pressure disturbance in air and/or Sound Pressure Level. Sound Pressure is the total instantaneous atmospheric pressure at a point, minus the static (average) pressure at that point, expressed in Pascals. Sound Pressure Level is 10 times the logarithm of the ratio of the time-mean square pressure to the square of the reference pressure. The standard reference pressure is 2 x 10^-5 Pa.

Industry/Application Area:
Forms the basis for the measurement of many acoustic parameters, including measurements of:

• Sound Intensity
• Sound Absorption
• Sound Power Level
• Sound Transmission Loss

Frequency Range of Interest:
Generally the range of human hearing, which is from 20 Hz to 20 kHz.

Units:

Sound Pressure (p) in Pascals
Sound Pressure Level (L_p or SPL) in decibels (dB) are 2 x 10^-5 Pa
May be expressed in terms of linear, frequency-weighted, 1/N-octave frequency brand or narrow frequency band (FFT) levels.

Tutorial Information
The measurement of sound pressure is based on the use of a microphone that is used as a transducer to create a voltage signal that is proportional to the root mean square pressure at the point in space where the microphone is located. This voltage signal can be used to study the amplitude and frequency of these pressure variations that create the sensation of sound. For tips on using microphones to make sound pressure level measurements, see Microphone.

Due to the large range of magnitudes of these pressure variations that humans can sense as sound (over 1:1,000,000), the voltage signal is typically passed though a logarithmic detector. A logarithmic detector approximates the response of the human ear to such pressure variations, and results in a measurement range that is reduced from a factor of a milling to 0 dB to 120 dB.

The result of the measurement is expressed as the sound pressure level, measured in decibels (dB), relative to a reference level (0dB=2x10^-5 Pascals).

The mathematical relationship is:

Lp = 20 * log p/pref

Where:
Lp = Sound pressure level
p = RMS pressure at the microphone
pref = a reference pressure of 2 x 10^-5 Pa

Test Environment
You can measure sound pressure levels in almost any environment. For measurements of basic acoustic properties of materials or equipment, you can typically make these measurements in anechoic, hemi-anechoic, free field, or reverberant test environments. In these controlled test environments, you can establish direct relationships between the sound pressure levels measured and the sound energy present.

When conducting sound pressure level measurements in other environments, the relationship between the sound pressure level and the total sound energy is more complicated. Measurements of basic equipment sound emission properties, such as sound power, in such environments result in higher measurement uncertainties, due to the unknown influence of the environment on the sound pressure levels measured.

Level Measurements
In most measurement situations, the sound pressure level of interest is a time-varying function. Measurement of the time-varying sound pressure level generally involves either averaging the sound pressure level over some fixed averaging period, or recording the sound pressure level versus time waveform, and performing analysis on the level versus time history.

Weighting of Sound Pressure Levels
Sound Pressure Levels are often expressed in terms of “weighted” levels. In this case, the principles of level and frequency measurement are combined to provide a single value that is representative of the overall level of the sound.

Weighting filters commonly used for sound pressure level measurements are known as A, B and C weighting networks.

Special Considerations for the Use of A-weighting
If you want to measure sound pressure levels to analyze the sound power emissions of a device, you often use octave or one-third octave band filtering. In these cases, the A-weighted level is often calculated from the individual band levels.

Errors Due to Uniform Corrections within a Measurement Band
One special consideration involves the fact that the A-weighted network is defined to be an analog filter with a continuous frequency response. When mathematically weighting a spectrum consisting of a proportional octave band data, the weighting values applied are equal to the A-weighted curve value at the proportional octave band center frequency. This creates an essentially rectangular filter that is not continuous in its response, and that applies the same correction to all energy with the band. If this mathematical correction is applied to a signal that contains a pure tone near one of the proportional bandwidth filter edges, a measurement error may be introduced. At frequencies below 500 Hz, where the slope of the A-weighting curve is quite steep, this error can be significant. This concept is illustrated below.

A second special consideration when calculating A-weighted levels from proportional octave band levels involves the measurement frequency range. As noted above, an A-weighting network has a continuous frequency response over the entire audio frequency range. However, when making proportional bandwidth measurements, you often limit the frequency range of interest to a bandwidth less than the entire audio frequency range. A-weighted levels calculated using this bandwidth-limited octave band data do not include the contributions of energy outside of the measurement bandwidth.

If you've selected the frequency range of interest properly for the Unit Under Test, then errors due to this special consideration will be minimal. However, in certain cases, you can encounter significant errors by ignoring the energy outside of the measurement bandwidth. For example, some Information Technology and Telecommunications Equipment (ITTE) emit significant energy in the octave band centered at 16 kHz. If you conduct a sound pressure level measurement of an ITTE device in 1/3 octave bands from 100 Hz to 10,000 Hz, and calculate A-weighted levels from these levels, you can have a significant error when compared to the level measurement through an analog A-weighting filter.
Approaches:

Approach 1
Average Sound Pressure Levels
Measurements involving noise (such as pink noise in a Transmission Loss Measurement) and measurements involving noise emissions of devices (such as Sound Power Level measurements) generally utilize an averaging method known as L_EQ averaging. The sound pressure over some fixed time interval is integrated and divided by the time interval, yielding a continuous steady sound that, within a given time interval, has the same mean-square sound pressure as the sound being measured.

The L_EQ of a time-varying sound pressure level sample is calculated as follows:

A typical L_EQ measurement period for measurements in building acoustics and product noise emissions is from 8 seconds to 1 minute. Longer time intervals may be necessary at very low frequencies.

Advantages/Disadvantages to Approach

+	Provides good information on average sound pressure level
+/-	Yields single result (per band) for each time interval
-	Loss of time history of signal eliminates time dependent analysis (that is, RT or SQ analysis)
-	Only provides meaningful information about sound energy when measurements made in controlled environments (that is, anechoic or reverberant chambers)

Industry Standards
ANSI S1.13, ISO 11201

Equipment

• Microphone(s) with uniform frequency response over frequency range of interest.
• Integrating, averaging sound level meter. This can be created using the virtual instrument hardware and software listed below in the Products section.
• Proportional octave band and weighting filters, such as A-weighting or C-weighting, may be useful

NI products commonly used for this measurement:

• PCI-4461
  
• LabVIEW
• Sound and Vibration Toolset
  
• NI 5911 Flexible Resolution A/D Converter
  
• PCI-4462
  
  Approach 2
  Level versus Time Measurements
  Measurements involving decay rates (that is, for sound absorption via reverberation time) and sound quality (that is, objective measures of subjective sound parameters) require the sound pressure level versus time history of the signal. Samples of the instantaneous sound pressure level are recorded at regular time intervals, and a level versus time history is created.
  
  Measurement of sound intensity is based on the measurement of sound pressure level versus time for two closely spaced microphones. In this case, the level versus time history of the sound pressure level signal is used to determine the phase relationship between the sound pressure level at the two microphones.
  
  

Advantages/Disadvantages to Approach

+	Provides detailed record of sound pressure level versus time over measurement interval
+	Preservation of time history of signal allows for analysis of time dependent parameters, such as reverberation time and sound quality.
+	Allows analysis of phase-dependent parameters on multiple signals (that is, transfer function or sound intensity)
+/-	Yields large amounts of data

Industry Standards
ANSI S1.13, ISO 11201

Equipment

• Microphone(s) with uniform frequency response over frequency range of interest.
• Sound level meter with level versus time capability, or data acquisition (DAQ) board with appropriate sampling rates. This can be created using the virtual instrument hardware and software listed below in the Products section.
• Proportional octave band may be useful

NI products commonly used for this measurement:

• LabVIEW
  
• NI 5911 Instrument for PCI
  
• Sound and Vibration Toolset
  

Related NI Products:

• Sound and Vibration Toolset
  
  Helpful Web Sites:
  
• Acoustic Test Chambers and Environments
  
• Measurement of Sound Absorption
  
  

Information Contributed By: David A. Nelson, P.E., INCE Bd. Cert. Nelson Acoustical Engineering, Inc. specializes in noise and vibration control, sound quality, laboratory facilities and test control systems, and instruction related to plants, buildings, laboratories, products, and machinery.

Reader Comments | Submit a comment »