The magnetic field generated by a pair of coaxial circular loops is analyzed in order to find the optimum separation between the loops for each value of a prescribed homogeneity. For the maximum heterogeneities considered here, 0.1%, 1%, and 10%, the optimum loop spacing is obtained following a graphical procedure so that the length of the homogeneous field region along the axis is the longest possible. This study is extended to regions near the axis and to the entire region surrounding the center, calculating the loop separation that produces the largest homogeneous volume. The field homogeneity of a pair of “Helmholtz” coaxial conical coils is also investigated to obtain the optimum spacing between the conical coils; the volumes calculated with the desired homogeneity are compared with those obtained with a single pair of optimum coaxial loops. A new arrangement is hereby proposed based on double conical coils with optimum separation between the coils and optimum aperture of the cones. Some of the proposed arrangements are carried out in the laboratory where the experimental results are in good agreement with the theoretical predictions.

In Hispania (present-day Spain and Portugal), there are 25 structures documented of classical Roman open-air theatres, of which 10 are in the south, in the Roman Baetica (Andalusia). The Baetica embraced the progress of urbanisation in the time of the Roman emperor Augustus, where theatres, built in stone, were the foci of entertainment, performance, and propaganda of the empire. The Roman theatre in Malaga presents the archaeological remains of the main vestige of the Roman Malaca. It is located in the historical centre of the city, at the foot of the hill of the Muslim Alcazaba and was discovered in 1952. It is a medium-sized theatre whose design corresponds to a mixed construction that combines making use of the hillside for the terraces, in the manner of Greek theatres, with a major construction where rock is non-existent, thereby creating the necessary space for the stands. In this paper, the production process, adjustment, and validation of the 3D model of the theatre are analysed for the creation of a numerical predictive model of its sound field. Acoustic properties of the venue are examined and the effect of the Muslim Alcazaba and the hillside on the various acoustic descriptors is analysed. The results highlight the influence of this large stone surface mainly on the time decay parameters.

An analytical study of the magnetic field created by a double-conical conducting sheet is presented. The analysis is based on the expansion of the magnetic field in terms of Legendre polynomials. It is demonstrated analytically that the angle of the conical surface that produces a nearly homogeneous magnetic field coincides with that of a pair of loops that fulfills the Helmholtz condition. From the results obtained, we propose an electric circuit formed by pairs of isolated conducting loops tightly wound around a pair of conical surfaces, calculating numerically the magnetic field produced by this system and its heterogeneity. An experimental setup of the proposed circuit was constructed and its magnetic field was measured. The results were compared with those obtained by numerical calculation, finding a good agreement. The numerical results demonstrate a significant improvement in homogeneity in the field of the proposed pair of conical coils compared with that achieved with a simple pair of Helmholtz loops or with a double solenoid. Moreover, a new design of a double pair of conical coils based on Braunbek’s four loops is also proposed to achieve greater homogeneity. Regarding homogeneity, the rating of the analyzed configurations from best to worst is as follows: (1) double pair of conical coils, (2) pair of conical coils, (3) Braunbek’s four loops, (4) Helmholtz pair, and (5) solenoid pair.