Determining the Acoustic Properties of Chihuahua, Manchego, and Panela Cheeses by Applying Ultrasonic Spectroscopy †

: In this paper, a study to determine the acoustic properties of Chihuahua, Manchego, and panela cheeses is carried out by applying acoustic spectroscopy in the ultrasound spectrum. The products were purchased at a local store in the capital city of Chihuahua. The echoscope block of the GAMPT ® acoustic tomograph with acoustic sensor at 2 MHz was used to measure the acoustic phase velocity (m/s), which depended on the thickness, with a quasiregular ambient temperature of 16 ◦ C. The acoustic tomograph used transmission with normal incidence. Measurements were performed in triplicate. The volumetric density and acoustic impedance of the cheeses, as well as the rheological properties, were determined through an indirect method. The results show that the acoustic phase velocities of the Chihuahua, Manchego and panela cheeses were APV Chi ≈ 1221.47 m/s, APV man ≈ 1436.05 m/s, and APV pan ≈ 1142.28 m/s, respectively. The volumetric densities of the Chihuahua, Manchego, and panela cheeses were ρ Chi ≈ 1.16 gr/cm 3 , ρ man ≈ 1.11 gr/cm 3 , and ρ pan ≈ 1.70 gr/cm 3 to 12.1 ◦ C, respectively.


Introduction
In Mexico, mainly cheeses made from bovine, goat, sheep, and buffalo milk are produced.Mexico stands out due to its great diversity of types of cheeses, with different geographical locations in the country associated with different types, such as aged, white, cotija, Chihuahua, fresh, Manchego, Oaxaca, and panela, to mention a few examples [1].Each one of them has a specific procedure for its manufacture and maturation [2].
Many investigations have been conducted on cheeses in general, From their nutritional and rheological (physical) properties [3], to the thermodynamic parameters that are fundamental for their manufacture, conservation, and maturity.
To discover some of the physical properties of cheeses, different excitation sources or methods have been used, such as low-intensity ultrasound.For example, in ref. [4], Lee et al. applied ultrasound to determine the rheological properties of cheeses by analyzing transverse plane acoustic waves.In [5], Benedito et al. applied ultrasound to determine the maturity of Mahon cheese.In [6], Mulet et al. determined the effect of temperature on the speed of ultrasonic propagation in cheeses.In [7], Benedito et al. determined the acoustic properties in the ultrasound spectrum of cheddar cheese.In [8], Wang et al. analyzed the functional properties of cheese by means of image processing.In [9], Cho et al. determined the physical properties of cheddar cheese through ultrasonic techniques, without contact.In [10], Benedito et al. analyzed the cheese-manufacturing process by means of ultrasound.In [11], Benedito et al. evaluated the texture of Manchego cheese by means of ultrasound.In [12], Leemans et al. described and determined the internal defects of the cheese structure.In [13], Nassar et al. studied the internal matrix structure of cheese by applying ultrasound.In [14], Telis-Romero et al. studied the composition of fresh cheese through ultrasound.In [15], Crespo et al. studied the quality of cheese made with sheep's milk by applying low-frequency ultrasound.
In this investigation, we present a study to measure the acoustic phase velocity of different commercial cheeses.

Materials and Methods
It was determined to measure the acoustic phase velocity of the cheeses as a function of thickness.A total of 15 products of Chihuahua, Manchego, and panela cheeses were purchased in a commercial store in the city of Chihuahua.The products were stored at a temperature of 4 • C for one week while the measurement experiments were carried out, in the biochemistry laboratory of the Faculty of Zootechnics and Ecology of Autonomous University of Chihuahua, (FZyE-UACh).

Experimental Setup
The measurements of the volumetric densities and acoustic phase velocities were carried out under the following thermodynamic conditions in the laboratory: open system; atmospheric pressure: 1023.0 hPa; humidity: 37%; laboratory temperature: 24.2 The volumetric density of the cheeses was obtained indirectly.Cuts were made into each cheese, where samples of parallelepiped geometry shapes of 1, 2, 3, 4, 5, and 6 cm thick were obtained, which were measured with a vernier (MITUTOYO ® , Kanagawa, Japan).Then, the mass of each of the samples was determined by means of a balance (Scout Pro, Ohaus ® , Parsippany, NJ, USA).This procedure was carried out for each of the fifteen pieces of cheese [16].
The thickness-dependent acoustic phase velocity was obtained by means of an experimental configuration of the transmission mode and applying the theory described by [17].Signal processing and filtering were performed using the echoscope's internal program.

Transmission Mode
In this configuration system, a laptop was connected via a USB-type connection to the echoscope of an ultrasonic tomograph (GAMPT ® , Merseburg, Germany 2016).From this, two 2 cm diameter ultrasonic sensors at 2 MHz were connected, with a transmitterreceiver configuration as shown in Figure 1.The excitation pulse was normal-incidence.The sampling rate was 100 MHz.Each of the cheese samples was placed on a support.Ultrasonic gel was used to match the impedance between the ultrasonic sensor and each of the cheese samples.
Acoustic phase velocity measurements depending on the thickness of each type of cheese, Chihuahua, Manchego, and panela, were performed every day.Each measurement was performed in triplicate.Acoustic phase velocity measurements depending on the thickness of each type of cheese, Chihuahua, Manchego, and panela, were performed every day.Each measurement was performed in triplicate.

Results
The properties of the cheeses were measured, such as the bulk density, which is described in Table 1.
In Figures 2-4, the graphs of the acoustic phase velocity in the different types of cheeses are shown.A linear fit was performed using the Origin 8.0 program (OriginLab ® , Northampton, MA, USA), with a confidence level of 0.95.

Results
The properties of the cheeses were measured, such as the bulk density, which is described in Table 1.
In Figures 2-4, the graphs of the acoustic phase velocity in the different types of cheeses are shown.A linear fit was performed using the Origin 8.0 program (OriginLab ® , Northampton, MA, USA), with a confidence level of 0.95.In Figures 5-7, the graphs of the acoustic transmittance as a function of frequency are shown for thicknesses of 1, 2, and 3 cm.In Figures 5-7, the graphs of the acoustic transmittance as a function of frequency are shown for thicknesses of 1, 2, and 3 cm.In Figures 5-7, the graphs of the acoustic transmittance as a function of frequency are shown for thicknesses of 1, 2, and 3 cm.In Table 2, the parameters obtained from direct and indirect measurements of the cheese samples are shown.In Table 2, the parameters obtained from direct and indirect measurements of the cheese samples are shown.In Table the parameters obtained from direct and indirect measurements of the cheese samples are shown.The results obtained with respect to the acoustic phase velocity of the cheeses have a linear behavior, where the Manchego cheese has a higher phase velocity than the Chihuahua and panela cheeses.However, the bulk density analysis demonstrates that panela cheese has a higher density than Chihuahua and Manchego cheeses.This is phenomenologically contradictory from the point of view of physics.A material with a higher bulk density may not have a higher acoustic phase velocity than one that has a lower bulk density.This means that, if the panela cheese has a higher density, it consequently has a higher acoustic phase velocity.However, it should be noted that the phase velocity was different in each of them.This influenced these measurements.Likewise, it is necessary to understand that the cheeses were of a commercial type, so the manufacturing, maturation, conservation, and distribution process is ignored until their use or consumption, and this is demonstrated by the results of the acoustic transmittance, where the spectra describe a non-homogeneity within the structure of cheeses in terms of frequency.In Table 2, the results obtained from the measurements are summarized.

Conclusions
The acoustic properties of commercial cheeses such as Chihuahua, Manchego, and panela were characterized.Until now, the acoustic properties of the cheeses studied did not appear in the reported literature, although there are acoustic results for other types of cheeses.Using acoustic pulses as excitation sources generates a greater scattering in the intrinsic properties of cheeses.It is possible to increase the sensitivity capacity of the experiments if this is done means of an adiabatic system.It is proposed that Chihuahua, Manchego, panela, and other cheeses should be produced by hand to characterize their acoustic and mechanical properties, and compare their results with the properties of commercial cheeses.

Figure 1 .
Figure 1.Experimental setup in transmission mode.

Figure 1 .
Figure 1.Experimental setup in transmission mode.

Figure 2 .Figure 2 .
Figure 2. Acoustic phase velocity dependent on the thickness of the Chihuahua-type cheese.

Figure 2 .
Figure 2. Acoustic phase velocity dependent on the thickness of the Chihuahua-type cheese.

Figure 3 .
Figure 3. Acoustic phase velocity dependent on the thickness of the Manchego-type cheese.

Figure 3 .
Figure 3. Acoustic phase velocity dependent on the thickness of the Manchego-type cheese.

Figure 4 .
Figure 4. Acoustic phase velocity dependent on the thickness of the panela-type cheese.

Figure 5 .
Figure 5. Acoustic transmittance as a function of the frequency of Chihuahua cheese.

Figure 4 .
Figure 4. Acoustic phase velocity dependent on the thickness of the panela-type cheese.

Figure 4 .
Figure 4. Acoustic phase velocity dependent on the thickness of the panela-type cheese.

Figure 5 .
Figure 5. Acoustic transmittance as a function of the frequency of Chihuahua cheese.

Figure 5 .Figure 6 .Figure 7 .
Figure 5. Acoustic transmittance as a function of the frequency of Chihuahua cheese.

Figure 6 .Figure 6 .Figure 7 .
Figure 6.Acoustic transmittance as a function of the frequency of Manchego cheese.

Figure 7 .
Figure 7. Acoustic transmittance as a function of the frequency of panela cheese.