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on several fruit and other products, such as: apple (ZUDE et al., 2004; YAMAMOTO ... BAERDEMAEKER 1993; CHEN, P. et al., 1992); tomatoes. (DUPRATet al.
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Antihus Hernández Gómez, Annia García Pereira, Jun Wang Acoustic impulse response potential to measure mandarin fruit ripeness during storage Revista Ciencias Técnicas Agropecuarias, vol. 15, núm. 4, 2006, pp. 24-30, Universidad Agraria de La Habana Fructuoso Rodríguez Pérez Cuba Available in: http://www.redalyc.org/articulo.oa?id=93215405

Revista Ciencias Técnicas Agropecuarias, ISSN (Printed Version): 1010-2760 [email protected] Universidad Agraria de La Habana Fructuoso Rodríguez Pérez Cuba

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Revista Ciencias Técnicas Agropecuarias, Vol. 15, No. 4, 2006

AGRICULTURA DE PRECISIÓN PRECISION FARM

Acoustic impulse response potential to measure mandarin fruit ripeness during storage Respuesta al impulso acústico para medir la madurez de la mandarina durante el almacenamiento Antihus Hernández Gómez1, Annia García Pereira1 and Jun Wang2 ABSTRACT. The aims of this research work were directed to evaluate the capacity of acoustic signal response to monitoring the mandarin fruit firmness change during storage. The dominant frequency, firmness index and elasticity coefficient as a function of time could be expressed as a decreasing polinomial function. A good correlation was established between the acoustic parameters (firmness index and coefficient of elasticity), and fruit compression force, for these data, the correlation coefficients were 0,88 & 0,91 respectively. The results indicates that it might be possible to identify the ripeness state of an individual mandarin by using the present method, and that the nondestructive acoustic test could replace conventional compression test in order to determine mandarin fruit firmness and expected shelf- life. Key words: acoustic impulse response technique, non-destructive test, firmness; ripeness, mandarin, storage. RESUMEN. Los objetivos de este trabajo investigativo estuvieron encaminados a evaluar la capacidad de la señal acústica para supervisar el cambio de firmeza de la mandarina durante el almacenamiento. La frecuencia dominante, el índice de firmeza y coeficiente de elasticidad pueden expresarse como una función de tiempo polinomial decreciente. Una buena correlación se estableció entre los parámetros acústicos (índice de firmeza y coeficiente de elasticidad), y la fuerza de compresión de la fruta, para estos datos, los coeficientes de la correlación fueron de 0,88 & 0,91 respectivamente. Los resultados indican que podría ser posible identificar el estado de madurez de una mandarina empleando el presente método, y que la prueba acústica no-destructiva podría reemplazar la prueba de compresión convencional para determinar firmeza de fruta durante la vida de estantería de la misma. Palabras clave: respuesta al impulso acústico, prueba no-destructiva, firmeza, madurez, mandarina, almacenamiento.

INTRODUCTION The acoustic impulse response method has been suggested by many researchers (ABBOTT et al., 1968, GALILI et al., 1998) to measure firmness as related to the elastic properties of fruits and vegetables. In this method, the fruit is excited by means of a hammer, and the response signal is captured using a microphone or/and film sensors.

From the spectrum of the response signal a firmness index is calculated. The development of low-cost, lightweight, and flexible piezoelectric film sensors, reported by (SHMULEVICH et al., 1996) added new possibilities for dynamic testing of agricultural products. They concluded that the sensor could detect the decreasing resonance frequency or the Firmness Index, during time, of the tested apples and of

Recibido 15/02/06, trabajo 88/06, investigación. Dr., Prof., Agricultural Mechanization Faculty, Havana Agricultural University, Cuba. E-:[email protected] 2 Dept. of Agricultural Engineering, Zhejiang University, Hangzhou 310029, China. 1

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Revista Ciencias Técnicas Agropecuarias, Vol. 15, No. 4, 2006

several other fruits during storage; and that the measuring technique of fruit firmness with the piezoelectric film sensors was found to be simple, fast, and repeatable. According with LANDAHL et al.,2002, the water loss has a considerable influence on the results of the acoustic impulse response technique. The proper values of impacting mass and drop height depend on the physical design of the sensing unit and the type of fruit being tested. Nondestructive firmness test would enable the firmness grading of every fruit and so result insignificant improvement in the control and specification of the firmness quality of fruit consignments. VAN WOENSELT et al., 1983, followed the ripening of apples, during their storage, using a wide band random vibrator of the range 0 to 1 600 Hz to excite the fruit. The excitation force was measured the vibrations on the opposite side. These two signals were used to detect the resonance frequency with the aid of FFT analyzer. The results showed a clear change in the Firmness Index during the entire season. An experimental system for nondestructive firmness evaluation, based on the flexible piezoelectric sensors, a microphone or and accelerometer was developed and tested on several fruit and other products, such as: apple (ZUDE et al., 2004; YAMAMOTO et al., 1980; VAN WOENSELT et al., 1988; LILJIDAHL and ABBOTT 1994; CHEN, H., and DE BAERDEMAEKER 1993; CHEN, P. et al., 1992); tomatoes (DUPRAT et al., 1997), avocado (PELEG et al., 1990 and GALILI et al., 1998); muskmelons (SUGIYAMA et al., 1994); watermelon (DIEZMA et al., 2004); pear (WANG, 2004, WANG et al., 2004; HERNÁNDEZ et al., 2004); peach (HERNÁNDEZ, et al., 2004); and many others. To indicate firmness for spherical fruit, stiffness factor (S) or firmness index (FI) (first introduced by ABBOTT et al., 1968, modified by COOKE and RAND, 1973) can be calculated as: S = f 2 m2/3

(1)

s ), f the where: S is the stiffness coefficient (kg dominant frequency where response magnitude is the greatest (Hz) and m the fruit mass (g). This stiffness factor is significantly correlated with fruit firmness and sensory measurements (GALILI and DE BAERDEMAEKER, 1996). To reduce errors caused by the variance in shape inherent in horticultural products, it is advisable to take the average of three measurements equally spaced on the fruit equator (CHEN, H. 1993). Modal analysis on spherical products (apples) has shown that the best signal is produced when the response is recorded 0 or 180° from the place of impact (HUARNG et al., 1993). RESEARCH of LANGENAKENS et al. ,1997, showed that the first resonance frequency for tomatoes corresponds with the oblate–prolate spherical mode, which appears not to be influenced by the internal compartment structure of the tomato. DE BELIE et al.,2000, in their research concluded that the acoustic technique is very reproducible, and its sensitivity to firmness changes was 2/3

-2

greater than that of the penetrometer; this technique was integrated into an automated fruit firmness monitoring system and tested successfully on ‘Jonagold’ apples in a commercial cool store. According with LANDAHL et al., 2002, the water loss has a considerable influence on the results of the acoustic impulse response technique. COOKE, 1972 and COOKE and RAND,1973, proposed a mathematical model for the interpretation of the vibrational behavior of intact fruit. They showed that the Elastic Modulus (or Young’s Modulus) could be estimated satisfactorily as fallows: E = f 2m2/3 ρ1/3

(2)

where: E is the elasticity coefficient (Pa) and ρ the density (kg/m3). Citrus fruit flesh generally is not as firm as that of other fruit, because of juice sacs. However, firmness is an important characteristic in citrus because the firmness of fruit flesh influences the mouth feel of citrus, (MURAMATSU et al., 1996. Most instrumental techniques to measure the firmness are destructive, involve a considerable amount of manual work, and they are not practical for cultivars or storage stations. However, little detailed information is available on firmness of mandarin fruit during storage using nondestructive impulse response (I-R). Therefore, the objective of this research work was directed to evaluate the capacity of acoustic signal response to monitoring the mandarin fruit firmness change during storage.

MATERIALS AND METHODS Mandarin «Zaojin Jiaogan» (C. reticulata) was selected to the experiment. All samples (200 samples) were taken directly from a simple same orchard and randomly assigned to be hand harvested at October 03, 2004, this date is consider as a mandarin commercial picking time. Upon arrival, each date the fruits were sorted and selected as samples according with a uniform color and medium size (672.5 mm). All fruits of each sample were individually numbered.

Mandarin storage conditions Two different storage treatments were performed; the mandarin fruit were matured under laboratory conditions (shelf live conditions). The mandarin fruits were placed in 4 vacuum plastic bags and carton boxes respectively, with 20 mandarins each one (total 80) to each treatment, it were stored for 12 days at 20 ± 0,5 ºC, relative humidity (RH) (60 %). Mandarin ((a bag/ a box) every time) were removed from storage at 3, 6, 9 and 12 days and evaluated. Forty samples prior storage (at harvest time) and after each storage interval time (20 mandarins) were subjected to compression test, immediately after mass, density and acoustic impulse response measurements.

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Revista Ciencias Técnicas Agropecuarias, Vol. 15, No. 4, 2006

Mass and density measurement The mass of fruit was determined with the Electronic Precision Balance (Mettler Toledo, Max. 1000± 0.01 g). The mass loss was determined over all individual fruit during each storage interval time. The percent of mass loss can be calculated as: ml= [(mi -mf)/ mi ] * 100 %

(3)

where: m1: mass loss, % mi : initial fruit mass, g mf : final fruit mass, g. The fruit density was measured by Archimedes’ principle using a purpose-built apparatus for fruit volumetric measurement by full fruit immersion in 1 l of clean tap water. Fruit were pre-wet, prior to placement in the apparatus, to minimize air bubbles forming on the fruit surface during immersion. Appropriate procedures and corrections were used to account for the volume of the suspension apparatus, and the fruit and water temperature. The density loss of each fruit was determined during each storage interval time. The density loss of fruit was determined using the next expression: l= [(i -f)/ i] * 100 %

(4)

where: 1 : density loss, % i : initial fruit density, g/cm 3 f : final fruit density, g/cm3. For the calculations were assumed a water mass density of 1 g/cm3.

The fruit firmness The fruit firmness was quantified by maximum compression force (Fc). The maximum compression force required to compress a fruit by 3 % of its diameter was recoded at a strain rates of 0.00016 m/s (10mm/min). The maximum compression force of all individual fruit was measured on the three positions along the equator approximately 120º between them, perpendicular to the stem-bottom axis. The measurements were carried out a Universal Testing Machine (Model 5543 Single Column, Instron Corp., Canton MA. USA). The test was performed using parallel plates to compression test.

EQUIPMENT Experimental equipment The acoustic signal was sensed by a piezoelectric transducer type sensor acceleration (CA-YD-139) with the following levels: sensitivity 0.05 PC/ms -2, maximum transverse ratio d 5 %, maximum velocity increment 105 ms-2, mass 5 g with a flat frequency response between 4 Hz-4 kHz, used sensor of force CL-YD-331, force

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impedance sensor with electrical sensitivity 3.7 PC/N: measure range: force 2000 N, traction force 100 N and inherent frequency 55 kHz. A multi channel combined type electrical amplifier YE5853 was used with a frequency range from 1 Hz to 200 kHz, with three bit and decimal system, transducer degree regulate, all different sensitivity tone can reach normalization process. Traduce sensitivity adjust range from 1- 10,99 PC/ unit. Maximum electrical input quantity 105 PC, output gain 1, 3, 10, 30, 100, 1 000 mv/unit (selected value 100 mv/unit). The sign was transferred to a computer (PC9801VM2, NEC) through an A/D converter (PCL- 1800). The sampling frequency was 1 kHz photoelectric switch used as an autotrigger in order to obtain the same timing of data acquisition. The data were analyzed by mean of Genie software (Interactive signal processing package) for Windows. This program gave a rapid visual depiction of the spectrum on the computer screen in function of time. The selected sound waves were imported to Microcal Origin 6.0 software, the response from time to frequency by means of Fast Fourier Transform (FFT), as demonstrated in fig. 1 a, b.

Measurements of acoustic signals response During the test, the fruit (mandarin) was first placed on a soft foam support in order to create free support conditions and not to disturb the vibration pattern. The frequencies were obtained with a piezoelectric sensor placed at opposite side of the impact point; the piezoelectric sensor was composed for a soft polyvinylidene fluoride (PVDF) film coated with thin layers of conductors that were bonded to a soft polyethylene-foam padding to allow free vibrations of the fruit. Fruits were then excited at the marked positions; the frequency of all individual fruit was measured on the three positions along the equator approximately 120º between them; the pendulum consist of a wooden ball of diameter 24.5 mm and a 150 mm long plastic rod. The weight of the pendulum was 12 g, the impact angle was of 45. It was light enough to avoid the damages. However, there may be slight damage if the same point receives repeated impact. In order to avoid this damage, it was verified that the location of the impact point did not affect the sound signals. Then, the impact point was periodically changed to minimize damage to the sample. The intensity of impacts at given point was limited to three repeated impact with a total, of 9 per fruit. In the resulting frequency spectrum, the first resonance frequency (f) was selected (DE BAERDEMAEKER, 1988; CHEN et al., 1992). Arbitrarily, only frequencies of which the peak amplitude was larger than 50 % of the overall peak amplitude were considered in this selection. Fig. 1b shows a typical frequency spectrum for a mandarin and the selected peak. Each signal was processed and normalized by maximum sound intensity. The Firmness Index was calculated by equation 1, and the Elastic Modulus (or Young’s Modulus) estimation was done using equation 2 (elasticity coefficient).

Revista Ciencias Técnicas Agropecuarias, Vol. 15, No. 4, 2006

FIGURE 1. Typical acoustic signal of Satsuma mandarin (mean 9 impacts): (a) time domain, (b) frequency domain.

RESULTS AND DISCUSSIONS Mandarin compression force behavior during storage The compression force in mandarin stored in bag and box are shown in Fig. 2. As can seen, in this figure depending upon the storage two-type treatments at the same temperature (20 C) the longer storage period gave the smaller Fc. The Fc loss of the fruits stored in bag was higher than the Fc loss of fruits stored in box.

carton box; it was minor due to the lowest weight loss in this period. The results of regression analysis between Fc and storage time for mandarin stored in bag and box are given in table 2,5. In both cases the compression force response to a polynomial equation, specified deg=2, moreover the relationship between the Fc and storage time for mandarin stored in plastic bag and carton box is high, which means that 97 and 98 % of the variation in Fc is explained by storage time. In citrus fruits, the relation between the degradation of the cellular wall and the loss of firm ness that accompanies fruit maturation has been observed as well (TING and ROUSEFF, 1986; MURAMATSU et al., 1996a).

Acoustic signal response to mandarin during different maturity states in storage

FIGURE 2 Compression force changes in mandarin according to storage time at 20 ºC and 55 % R.H.

At the end of twelve days storage period the highest Fc loss was obtained (22,89 N) from the fruits in carton box and the lowest Fc loss was obtained (17,68 N) from the fruits stored in plastic bag. The average of compression force loss every three days it was 4.42 and 5,68 N for mandarin stored in bag and box respectively. The compression force values of mandarin rapidly decrease during their first six storage days (day 3 & day 6) after this time the fruit compression force slowly decreased during the rest of intervals. It is also shown that the fruit Fc loss value descends from 4,62 and 8,1 N in the first three day down to a 0.61 and 0.23 N in its last three storage days in bag and box respectively. Moreover, the compression force loss during the last three days of the mandarin kept in

The figures 3a, b & c, show the change of the frequency, firmness index and elasticity coefficient against time, during Satsuma mandarin ripeness in storage at 20 ºC and 552 % RH for each storage type or treatment. The higher f, FI and E corresponds to the firmer mandarins prior storage. The frequency in mandarin stored in bag and box are shown in Fig. 3a. As can seen, in this figure depending upon the storage two-type treatments at the same temperature (20 C) the longer storage period gave the smaller resonant frequency. However starting from the sevenobservation day for the mandarins stored in carton box a light increased in frequency can be observed. This phenomenon can be associated to the high fruit water lost value due to the fruit was exposed to the surrounding air bring to as a consequence an excessive drying of the mandarin; due to high dehydration the skin loss its natural turgor, this phenomena is accompanied with the peel creasing and an increment of the skin resistance to penetration. Due to this phenomenon the resonant frequency, increase its values at the last observation, not meaning this that the internal mandarin firmness increased with storage time. In the reality, the mandarin firmness measured through of compression force deceased all the time.

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Revista Ciencias Técnicas Agropecuarias, Vol. 15, No. 4, 2006

FIGURES 3a, b & c. Changes in mandarin mean frequency value during its ripening in storage (20 mandarins).

The resonant frequency values of mandarin stored in bag, decrease during whole storage time from 375 to 287 Hz. This result means a frequency decrease of 23,32 % during all storage time. During the three first days can be see a quickly change in frequency with a fall of 43 Hz this value represent 11,27 % of the total frequency lost. After this period a moderate decreased in frequency, change is observed. The average of frequency loss every three days it was 22 Hz (5,83 %) for mandarin stored in bag, this result infers that the decrease in resonant frequency for each fruit is 1,94 % per day. The results of regression analysis between puncture force and storage time for mandarin stored in bag and box are given in Table 1. In both cases the resonant frequency response to a polynomial equation, specified deg=3, moreover the relationship between the frequency and storage time for mandarin stored in plastic bag is good, with a determination coefficient of 0,98, which means that 98 % of the variation in frequency is explained by storage time. TABLE 1. Regression analysis results between each mandarin acoustic parameters and storage time (20 mandarins) Equation

R2

P

SD

0,98013

0,17887

9,59171

0,98992

0,12759

0,13217

0,98922

0.13194

0,13769

0,99997

0,00729

0,01017

0,99866

0,04652

0,06749

0,99967

0,02327

0,00275

Storage in bag f= 373,93357- 16,04821d + 1,47325d2- 0,06194d3 2

3

FI=3,14266- 0,18806d+ 0,00703d - 1,57685e-5d 2

E= 0,30522- 0,01783d+ 5,95861E-4d + 5,5328e-6d

3

Storage in box f= 375,1652- 33,89789d+ 2,93869d2- 0,07256d3 2

3

FI= 3,17258- 0,55545d + 0,05909d - 0,0021d 2

E= 0,30733- 0,05387d + 0,00558d - 1,94444e-4d

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The Fig. 3b shows the firmness index behavior of mandarin as storage time function. The FI of mandarin has a decline during whole observation time. The firmness index values fall from 3,16 to 1.93 *104 kg2/3s-2 and from 3,16 to 1,38 *10 4 kg 2/3s -2 in mandarins stores in bag and box respectively. This result mean a diminution of 39,92 % and 56,32 % in the firmness index value respective to its initial values (at harvest time) during whole storage time. The firmness index average value for each interval of storage time (3 days) was 0.31 and 0,45 *104 kg2/3s-2 in mandarins stored in bag and box respectively. The decrease in the firmness index during the last three observation days in mandarin stored in carton box only archived a 3,37 % of the total, consequently with the increase of the resonant frequency in this period. The firmness index of mandarin decrease during their perma nence in storage, a ccording to third-degree polynomial curve, see table 1 for each storage treatments. The relationship between FI and storage time is excellent, with a determination coefficient of 0,98 and 0,99 in mandarin stored in bag and box respectively. The Fig. 3c shows the elasticity coefficient behavior of

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mandarin as storage time function. The coefficient of elasticity of mandarin has a decline during whole observation time. Its values fall from 0,31 to 0,19 MPa and from 0,31 to 0,13 in mandarin stores in bag and box respectively. This result means a diminution of 56,32 % and 58,31 % in the elasticity coefficient value respective to its initial values (at harvest time) during whole storage time. The E average value for each interval of storage time (3 days) was 0,03 and 0,04 MPa in mandarins stored in bag and box respectively during all storage time. The firmness index of mandarin decrease during their perma nence in storage, a ccording to third-degree polynomial curve, see table 1 for each storage treatments. The relationship between E and storage time is excellent, with a determination coefficient of 0,98 and 0,99 in mandarin stored in bag and box respectively. On the contrary to frequency, the firmness index an elasticity coefficient decrease its values during all mandarin storage time in bag and box, give it the true behavior of the fruit firmness during storage. The change in fruit firmness more significant was given by elasticity coefficient; the elasticity coefficient values overcoming in 0.16 and 1,98 %

Revista Ciencias Técnicas Agropecuarias, Vol. 15, No. 4, 2006

the values of firmness given by the firmness index in mandarins stored in box and bag respectively during the 12 days of mandarin storage time. For what it, can be considered the elasticity coefficient as the best indicator of the fruit firmness when the acoustic signal response technique is used to measure the firmness of the fruit during storage periods. In mandarin stored in box high fruit water lost values can be observed, due to the fruit was exposed to the surrounding air, bring to as a consequence a excessive drying of the mandarin skin. This desiccation phenomenon gave an increase of the fruit internal resonant frequency, but this doesn’t mean that the fruit firmness given by the firmness index and elasticity coefficient diminishes consequently with the storage time. It can be concluded that the acoustic response technique is also efficient to measure the mandarin firmness when the fruit is stored in carton box. The mandarin ripening in bag is characterized for a progressive decrease in the frequency, firmness index and elasticity coefficient. The higher f, FI and E corresponds to the firmer mandarin prior storage. In the case of the mandarin stored in box a different behavior was observed to the last tree days of observation with an increase of the frequency in the case of firmness index and elasticity coefficient can be express the true firmness behavior. Same result was found by DUPRAD et al., (1997), in Golden Delicious apples. They showed that the acoustic response of the fruit fall with storage time. The fruit ripening in storage is characterized for a progressive decrease in the frequency, firmness index and

elasticity coefficient. The higher f, FI and E corresponds to the firmer fruit prior storage. The change in fruit firmness more significant was given by elasticity coefficient. For what can be considered the elasticity coefficient as the best indicator of the fruit firmness when the acoustic signal response technique was used to measure the firmness of the fruits during the storage periods. For this reason it is recommended to use the firmness index and elasticity coefficient to study the firmness behavior of the fruit during their storage live. Regression was carried out with the means of 20 determinations of each mandarin parameter except in the beginning (start day/ day 0) where were took 40 samples.

CONCLUSIONS • The firmness index and elasticity coefficient were clearly identified and steadily decreased with storage time, for what can make sure that the Acoustic impulse Response gives a reliable indication of the change or/and ripeness status of mandarin fruit during the storage conditions. • A negative strong correlation was found between each mandarin acoustic analyzed parameters and storage time. In all cases, the process was characterized by polynomial model. • T h e n on dest ruct i ve a coust i c t est m a y r epla ce conventional destructive test mandarin in order to determine fruit firmness and expected shelf- life. • No sing of bruising was observed in the fruits tested, during and after the experiments, confirming the nondestructiveness of this technique.

REFERENCES 1. ABBOTT, J.A. et al.: «Sonic techniques for measuring texture of fruit and vegetables», Food Technol., 22, 635–645, 1968. 2. CHEN, H.: «Analysis on the acoustic impulse resonance of apples for non-destructive estimation of fruit quality», Ph.D. thesis dissertation, Katholieke University, Leuven, Belgium, 1993. 3. CHEN, H. and J. DE BAERDEMAEKER: «Effect of apple shape on acoustic measurements of firmness», J. Agr. Eng. Res., 56, 253–266, 1993. 4. CHEN, P.; Z. SUN and L. HUARNG,: «Factors affecting acoustic responses of apples», Trans. ASAE, 35, 1915–1992, 1992. 5. COOKE, J.R.; R.H. RAND: «A mathematical study of resonance in intact fruit and vegetables using a three media elastic sphere model», J. Agric. Eng. Res., 18, 141–157, 1973. 6. DE BELIE, N. et al.: « Development of an automated monitoring device to quantify changes in firmness of apples during storage», Postharvest Biol. Technol., 18, 1–8, 2000. 7. DUPRAT, F. et al.: «The acoustic impulse response method for measuring the overall firmness of fruit», J. Agric. Eng. Res., 66, 251–259, 1997. 8. GALILI, N. and J. DE BAERDEMAEKER : «Performance of acoustic test methods for quality evaluation of agricultural products», In: ISMA Conference, September 1996, Leuven, Belgium, 1996. 9. GALILI, N.; I. SHMULEVICH and N. BENICHOU: « Acoustic testing for fruit ripeness evaluation», Trans. ASAE, 41, 399–407, 1998. 10. HERNÁNDEZ, A. et al.: «Acoustic testing for peach fruit ripeness evaluation during peach storage stage», Revista Ciencias Técnicas Agropecuarias, vol. 11, no.3, 2004.

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11. HERNÁNDEZ, A.; J. WANG, and G. GARCÍA: «Impulse response of pear fruit and its relation to Magness-Taylor firmness during storage», Postharvest Biology and Technology, 35, 209-215, 2005. 12. HUARNG, L.; P. CHEN and S. UPADHYAYA: «Determination of acoustic vibration modes in apples», Trans. ASAE, 36, 1423–1429, 1993. 13. MURAMATSU, N. and T. TAKAHARA: «Relationship between texture and cell wall polysaccharides of fruit fresh in various species of citrus», Hort. Science, 31, 1, 114-116, 1996. 14. PELEG, K.; U. BEN-HANAN and S. HINGA: « Classification of avocado by firmness and maturity», J. Text. Stud. 21, 123–129, 1990. 15. SUGIYAMA, J.; K. O. SHAYASHI and S. USUI: «Firmness measurement of muskmelons by acoustic impulse transmission», Trans. ASAE, 37, 1235-1241, 1994. 16. SHMULEVICH, I.; N. GALILI and D. ROSENFELD: «Detecting of fruit firmness by frequency analysis», Trans. ASAE, 39, 1047– 1055, 1996. 17. WANG, J.: « Mechanical properties of pear as a function of location and orientation», Inter. J. Food Prop. ,7, 155–164, 2004. 18. WANG, J.; B. TENG and Y. YU: «Pear dynamic characteristics and firmness detection», Eur. Food Res. Technol., 218, 289–294, 2004. 19. YAMAMOTO, H.; M. IWAMOTO and S. HAGINUMA: « Acoustic impulse response method for measuring natural frequency of intact fruits and preliminary applications to internal quality evaluations of apples and watermelons» J. Text. Stud., 11, 117–136, 1980.

La Universidad Autónoma Chapingo y su Departamento de Ingeniería Mecánica Agrícola felicitan a la RCTA, por sus 20 años al servicio de la información científica y técnica

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