Sound Response By Carleen Trott: The Physics Of The Cremer

Trott studied the input admittance and transfer admittance at the soundpost positions on the top and back plates in the absence of the soundpost. He studied a well documented violin by Carleen Hutchins, SUS 181, and provided the plot of sound response as well as the input admittance of the instrument complete with soundpost. This violin had also been studied by Beldie [32] who published sound pressure level, (SPL), and admittance plots which can be compared with those of Trott. The phase plot is also included by Trott. It can be seen that there is a peak at the position of the lower air resonance in all admittance plots in Trott’s paper but at a lower frequency when the soundpost is missing. The Helmholtz resonance appears as the next minimum
Since the violin is not grounded in the strict engineering sense, the question of the relative phase of the various parts such as the plates and sides, has not received a consistent treatment. Cremer has regarded the holding of the violin at the shoulder as a “lossy” spring support. The relative phase of the motion of the different parts of the violin is of main concern below 1 kHz where the breathing action operates. Meinel [23] and others have related the phase to the centre of gravity of the violin. Motion to or from the centre of gravity is taken as in phase. Beldie’s 4 mass (4 spring) model of the violin at low frequencies has been reviewed by Cremer [19]. The four masses are the top, sides, the back (including the soundpost and a small section of the top in contact with it) and the air enclosed. The four corresponding springs are placed between the top and the “island” at the soundpost, at the margins of the top and back plates and the stiffness of the air. Cremer’s fgures 10.2 and 10.9 summarising this model and its application to the low frequency behaviour has been reproduced here as Figure 3. The sides are in phase with the plates i.e. all moving in and out together, at A0 and from approximately 400 to 600 Hz. There are antiresonances at about 300, 500 and 700 Hz. The soundpost is assumed
The extent of rib flexing is not expected to be large and would be restricted by the need to maintain the glue joint between the ribs and the plates. Studies have shown bending either along or across the ribs. Hutchins [36] shows a series of holograms for SUS 182 taken prior to 1971 that include the ribs with indication of bending though difficult to interpret. More recently Molin et. al. [37] have published holograms for five prominent body modes that show the rib bending more clearly (reproduced in Figure 4). The three lower modes show bending along the rib edges in the centre bout while the two higher modes suggest bending across the ribs near the corners. While the trendline may be mass like, at body resonances rib bending stiffness will combine with soundpost stiffness in determining the frequency.

Cremer [38] took up consideration of the soundpost and the “ring” mode in the back at 650 Hz. He likened the soundpost to a spring coupling two masses and compared the inverse admittance of the violin body with the stiffness impedance of the soundpost, i.e. ignoring its mass. The comparison did not lead to the result he expected. Trott’s work suggests a crossing would occur at a frequency above 800 Hz, the limit of Cremer’s figure. Is the comparison valid in this case, since the soundpost is