Measurement configurations

µZ works in two different configurations:

• 4 microphone mode

• 5 microphone mode

The difference is the presence of a tip microphone, which measures the sound that passes through the sample. Depending on the sample characteristics, one or the other method is preferred. How the configurations work is outlined below, including guidelines how to select the best configuration.

4 microphone mode

Inner workings

This configuration only uses the 4 MEMS microphones that come pre-assembled along the length of the main tube. The system uses plane wave decomposition on the soud field inside the tube, to extract the wave that travels from the loudspeaker to the other end of the main tube -at which a sample could be mounted- and the wave that is reflected and travels back. From this information, it calculates:

• reflection coefficient
• absorption coefficient
• input impedance

The input impedance is the impedance seen at the sample end of the main tube. It includes the sample holder and radiation impedance.

If the properties of only the sample itself need to be determined, a measurement of a sample can be combined with a measurement of an empty sample holder: the reference measurement. These have the same input impedance, except for the contribution of the sample. ACME can combine the measurements to extract the series impedance of the sample.

5 microphone mode

The characteristic impedance of the tube is given by¹:

$$Z_0=\frac{z_0}{S_{\mathrm{tube}}}\approx \frac{412\mathrm{Rayl}}{\frac{\pi }{4}{D}_{\mathrm{tube}}^2}$$

where $z_0$ is the characteristic specific acoustic impedance of air (MKS Rayl), $S$ the inner cross-section of the tube (m${}^2$) and $D$ the inner diameter of the tube (m). The units of $Z_0$ are Pa$\cdot$s/m${}^3$.

For samples with a higher impedance than 20$\times Z_0$, the plane wave decomposition method by itself is not sufficient achieve good results over the entire frequency range. The acoustic volume velocity through the sample is so small than it cannot be determined with a good relative accuracy. It must be measured in a more direct way. This is done using an additional microphone in a cavity behind the sample. The microphone capturing the signal is called the tip microphone. The pressure measured in the back cavity is used to determine the volume velocity through the sample, which in turn is used to calculate the sample's acoustic properties.

Back cavity size

The pressure levels measured at the tip microphone are determined by the size of the back cavity. Therefore, the ideal back cavity size depends on the specific sample that's being tested. µZ-20 comes with cavities in two sizes:

• 0.5 cc: This is the default cavity.
• 0.1 cc: This cavity is suitable for samples with the highest impedances. With the extra small cavity size, only a tiny volume flow is required to get a usable signal at the tip microphone.

Choosing the most suitable measurement configuration

An overview or use cases for both measurement configurations are shown in the table below. The diameter is only a rough guideline.

The provided guidelines are all qualitative as the combination of a specific acoustic impedance, with a certain cross sectional area combined result in a series impedance. If no information is available about the sample under test, the following procedure can be followed:

1. Measure the series impedance in the 5 mic (0.5 cc) configuration.
2. If ACME warns that the signal on the tip microphone becomes too low, re-measure in the 5 mic (0.1 cc) configuration.
3. If ACME showed no warning, plot the Input impedance, normalized to Plane wave impedance. The value should be larger than 10$\times$ (20 dB). If not, re-measure in the 4 mic configuration.

The 4 microphone mode is suitable for low-impedance samples with respect to the characteristic impedance of the tube.

1. when we specify Rayl , we always mean MKS Rayl. 1 Rayl is 1 Pa$\cdot$s/m ↩