## 1 Introduction  
In the framework of architectural restoration of cultural heritage, an accurate knowledge of material properties is essential in order to design proper interventions. The aim of restoration works is to preserve the artifacts and increase the safety and then the life span of existing buildings and their structures. In this context, deep knowledge of the constituent materials, with their interaction with environmental loads and the degradation effects on the mechanical properties, is crucial to diagnostic operations [1, 2, 3]. Investigations aimed at estimating the mechanical properties of construction materials can be of different types. Working on historical structures, and in particular on architectural heritage, however, it must be considered that the material characterization process requires the use of specific non-destructive techniques (NDT) in order to avoid possible damages. For this reason, in the last decades different approaches were developed to increase the mechanical and physical knowledge of the structures and the constituent materials [4, 5, 6, 7]. Moreover, it must be considered that historical constructions are mainly made from masonry, a complex heterogeneous material whose mechanical behavior is strongly dependent on the properties of the mortars and blocks and by their arrangement. In this framework, the research on appropriate non-destructive techniques, especially related to the on-site tests, for the characterization of masonry is still a challenge [8, 9, 10, 11, 12, 13, 14, 15]. Among the NDTs generally used on structural materials, impact, sonic and ultrasonic tests have received particular interest due to the non-invasive methodology and, at the same time, the ability of providing several types of information regarding the material condition. Sonic, ultrasonic and impact tests are based on the analysis of the elastic waves propagation through the material, from which several features can be derived, such as the presence of damages, the status of the degradation, or the estimation of the elastic parameters. Owing to the common assumption made in the sonic tests, which considers the material as elastic, isotropic and homogeneous, most of the works reported in the literature concerning Civil Engineering applications are referred to concrete material. This is due to the small characteristic length of the microstructure with respect to the dimension of the structural element, allowing to consider concrete material as almost homogeneous [16; 17; 18; 19; 20; 21; 22]. The application of sonic and impact tests on masonry material is still today controversial in the scientific community, due to the uncertainties and the strong randomness of masonry in historical constructions. However, several papers can be found in literature, especially regarding the comparison between damaged and undamaged masonry panels, e.g., to verify the effectiveness of restoration works, or to analyze the internal texture, and also detect and localize the presence of voids [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. The aim of this work is to study the use of impact tests on masonry material for the estimation of the elastic parameters by means of classic homogenization approaches for the characterization of heterogeneous media, which are based on the analysis of test windows [34; 35; 36; 37; 38; 39; 40; 41; 42]. More in detail, the novelty of this study is to investigate the effectiveness of estimating the elastic modulus of the material by analyzing the propagation velocity of the elastic waves with the increase of the structural element dimensions on which the tests are performed. The applications reported in this work are based on the study of both direct and indirect test, i.e., on the analysis of volume (P-wave) and surface (R-wave) elastic waves.