On the sound production of the timpani LAMBERTO TRONCHIN, ALESSIO BUTTAZZONI AND VALERIO TARABUSI DIENCA – CIARM, University of Bologna, Italy http://www.ciarm.ing.unibo.it Abstract: - The acoustic features of kettledrums through modal analysis and acoustic radiation measure were investigated. Modal analysis exciting the system by a hammer and a shaker on two different kettledrums was studied. Through this analysis 15 vibration modes were found. Their mappings resulted very clear and defined. Acoustic radiation using two different parameters was measured. The first parameter, v p / , has been already used to measure acoustic radiation of the soundboard of a piano (Giordano), and of a harpsichord (Tronchin et al). The second, v p ⋅ , is a new parameter called intensity of acoustic radiation. This parameter resulted more linked to the frequency response function than v p / . Keywords: - Timpani, Kettledrum, Modal analysis, Intensity, Acoustic radiation. 1. INTRODUCTION Kettledrum is the only orchestra drum that can produce defined pitch notes. For this reason many physicists investigated its acoustic features coming to interesting results, that however can be improved. In this work, studies on modal analysis and on the measure of acoustic radiation of kettledrum using different techniques were performed. Two different kettledrums were analysed, by means of two different ways of excitation of the system (hammer and shaker). The acoustic radiation ( v p ⋅ ) was measured and compared to ( v p / ) used in studies on the soundboard of the piano and of the harpsichord. In such a way, the generation of sound of musical instruments with vibrating surfaces (as the membrane or the soundboard) was better measured. 2. TIMPANI PHYSICS Timpani are the most important instruments among orchestra drums, because they produce definite notes. Real or ideal membrane is similar to a string. The string frequency and the membrane frequency are both directly proportional to the square tension and inversely proportional respectively to the string’s length and the membrane’s diameter. The basic difference between a string and a membrane is that the string’s partials are harmonic, while the membrane’s partials are not harmonic. Membrane’s surface static zones, called nodes are not punctiform, as string’s nodes. Membrane’s nodes are circular lines concentric to the circumference and straight lines that correspond to the diameters of the membrane itself. Each partial composing the sound of the instrument corresponds to a specific membrane vibration mode. The number and the type of nodes they are made of conventionally define vibration modes. For example is called (0,1) the first vibration mode of an ideal membrane, characterized by a circular node correspondent to the circumference itself with no diametrical node. Some physicists investigated how could kettledrum produce a defined pitch note. Lord Rayleigh, A. Benade and T. D. Rossing, in particular, found some hints to answer this question. In 1877 Lord Rayleigh in his treatise The Theory of Sound, explains the important limiting effect of the kettle on the movement of air in touch with the inferior surface of the membrane [1]. He was one of the first who studied how the influence of air can modify membrane vibration. Rayleigh noticed that the main sound of kettledrum corresponds to the second partial: (1,1) mode. Thanks to the experiences he made with a 25 inches (65 cm) kettledrum, Rayleigh found three following partials respectively far one to the other of a fifth (1,5 frequency ratio), a major seventh (1,89 f.r.), and an imperfect octave (about 2 f.r.) and he thought them linked to the (2,1), (3,1) and (1,2) modes. Arthur H. Benade in 1973 found the first ten components of the sound using a 25 inches kettledrum tuned on the Do note (130.8 Hz) and he found them in harmonic ratio with a missing fundamental an octave below the audible sound [2]. Rossing (in several studies from 1982 to 1998) and the staff of the Northern Illinois University investigated vibration modes of the kettledrums using modern instrumentations. They discovered that all the vibration modes