Precise Measurement of the Sound Pressure Level Frequency Response
in Presence of Room Modes
Introduction / Problem Solving:
A chassis in free air produces simultaneously positive and negative sound pressure waves which cancel each other in some distance. Such room resonances (superimposed waves traveling in opposite directions, a.k.a. room modes) will not be excited. The situation becomes complex as soon as the chassis is mounted in its enclosure and excites room modes.
The usual method of measuring the frequency response of the Sound pressure level (SPL) of a chassis in an enclosure uses time gating. The time window in which the sound pressure is recorded is set such, that the reflections of the sound from the walls and room modes are excluded from the measurement.
The time domain measurement is then transformed into the frequency domain in order to get the frequency response of the SPL. Because of the transformation the time window results in the achievable frequency resolution of the measurement.
In most laboratories the distance from the chassis under test to the next wall is below 2 meters. As the sound travels 343m per Second, the first reflection from the wall arrives after about 11 Milliseconds. A corresponding time window set to 10m Seconds corresponds to a frequency resolution of 100 Hz.
It becomes clear from this realistic example that frequency measurements below 1 kHz are not possible with acceptable frequency resolution and accuracy.
A further problem persists, as the noise level in a standard laboratory is usually too high to allow high dynamic microphone measurements.
The AudioChiemgau Room Mode Compensator enables the measurement of the SPL with high frequency resolution (e.g. 0.1 Hz) and high accuracy down to 10 Hz expanding simultaneously the dynamic range of the measurement.
Its basic principle is to eliminate the room resonances and environmental noise from the time domain measurement. For this purpose two microphones are used to distinguish the direct sound from the chassis to be measured from the unwanted room reflections and ambient noise.
Such the time window can be set according to the desired frequency resolution of the frequency measurement. Usually a time window of 10 Seconds is used in order to get 0.1 Hz frequency resolution.
Room Modes: Why do they exist?
The simplest case: Parallel room boundaries (walls, floor and ceiling)
A sound wave is reflected back and forth between parallel room boundaries.
At a certain wavelength λ = 2 × L (L = room length, width or height) both waves superimpose in phase und deliver a so called standing wave. The frequency at which this happens, is a resonance frequency or „mode“ of the room.
If the distance of the parallel room boundaries is a multiple of the half wavelength „standing“ waves build up, which result in a significant sound pressure increase at their antinodes.
The sound pressure has always its maximum (antinodes) at the room boundaries (the molecule velocity is zero at a hard boundary, resulting in maximum sound pressure).
Room Modes: Why do they disturb acoustical measurements?
Measuring the Sound Pressure Level (SPL) frequency response of a loudspeaker
In order to avoid variations of the SPL coming from room resonances, usually the measurement microphone is placed very close to the membrane of the loudspeaker to be tested.
Nevertheless the room resonances (room modes) and the resulting variations of the SPL significantly disturb the measurements.
The frequency responses below illustrate that problem:
Green: The real SPL frequency response of the device under test (DUT)
Blue: Measurement microphone 5cm from the membrane
Violet: Measurement microphone 100cm from the membrane
The increase of disturbing room modes with microphone distance is clearly visible. With increasing microphone distance one measures the room, but not the loudspeaker.
Room Modes: Solutions to that measurement problem
1. A solution to that measurement problem is using an anechoic chamber.
However the acoustical wavelength at low frequencies is very long (16 Hz correspond to a wavelength of 21m).
In order to absorb these low frequencies, an absorber needs to be placed at a quarter wavelength in front of each acoustical boundary (walls, ceiling, floor), i.e. at a distance of approximately 5m. This requirements leads to very large and expensive anechoic rooms. Smaller dimensions limit the usable low end frequency response.
2. An alternative and often used method is time gating. A time gate is set such, that the sound reflections from the room boundaries arrive later than the end of the time gate and are such excluded from the evaluation of the measurement. However a short time gate as necessary in normal laboratories (around few 10ms) limits the measurement resolution, which is the inverse of the time gate duration (e.g. 10ms time window correspond to 100 Hz frequency resolution). Such it is not possible to measure below approximately 1 kHz with sufficient frequency resolution and SPL accuracy.
3. Other solutions to that measurement problem are e.g to measure firstly a room transfer function and correct afterwards the measurement of the test object. This is not very practically and not accurate at all.
4. Also known is the three dimensional scanning of the SPL along a virtual hull around the loudspeaker and calculating the SPL frequency response from that.
A long duration measurement requiring a precise three dimensional mechanical scanner and expensive evaluation software make this approach complex and expensive.
The picture shows how B&O solves that problem with the „Cube“, an extremely large room, which allows to set the time window sufficiently large. Obviously a very expensive solution.
AudioChiemgau solution to that measurement problem
AudioChiemgau offers a simple technology solving the discussed measurement problem:
The loudspeaker is measured in the near field at 5 cm between membrane and measurement (direct) microphone and simultaneously the room modes are measured with a second microphone (mode microphone) in 5 cm distance between the two microphones.
Both microphones record the direct sound pressure from the chassis and the room modes according to the
inverse proportional law.
The SPLs of the direct sound are significantly different
for both microphones, as the relative distances from the source (loudspeaker membrane) are significantly different.
The SPLs of the modes are practically equal, as the sound wave traveled already quite some distance before arriving at the microphones. The same argument holds for environmental noise.
The ModeCompensator uses this physical relationship and calculates in real time a mode free SPL signal from the loudspeaker under test.
Example above: iMac with FUZZ Measure and Clarett USB audio Interface
The following measurement shows the SPL frequency responses of the chassis with ± 0.1 dB SPL accuracy and
0.1 Hz frequency resolution measured in a standard laboratory (logarithmic sweep time is 10 Seconds and time gate is 10 Seconds).
Red is the measured SPL of the direct microphone in the near field of the membrane.
Violet is the measure SPL of the mode microphone close to the chassis.
Blue is the mode free SPL frequency response derived from the above two measurements using the ModeCompensator.
The visible low end frequency limit is resulting from the loudspeaker under test (-3 dB @ 15 Hz).
The figure below shows the extended dynamic range the ModeCompensator offers. As the modes also any environmental noise is significantly reduced. This allows high dynamic measurements of the linearity, here the second (solid line)and third (dashed line) harmonics of the chassis. For that measurement an AudioChiemgau MFB controlled SEAS L22 chassis was used. The frequency range extends to 15 Hz (-3dB). The harmonic distortions are below 50 dB (0.3%) above 20 Hz and below 60 dB (0.1%) above 30 Hz. This chassis would be used as woofer between 15 Hz and 200 Hz. Measurements like these are extremely difficult or even impossible without the AudioChiemgau ModeCompensator.
ModeCompensator Block Diagram and I/O Specification
The ModeCompensator is available and may be ordered from AudioChiemgau.
See here for more details of this essential labratoy equipment.