Calculating the acoustic input impedance of a simplified brass instrument as an educational laboratory activity.

The concept of acoustic impedance is often difficult for students in introductory acoustics courses to make sense of, especially students without advanced mathematics backgrounds. This work summarizes a laboratory activity for students in a general education musical acoustics class where a simplified brass musical instrument is examined, focusing on how the geometry of the air column affects the input impedance of the instrument. Students are guided through making bore profile measurements for use in a computation of the input impedance. Options for making experimental measurements of the simplified instrument are explained. The laboratory activity was successfully used with students who reported their increased understanding of the acoustics of brass musical instruments.

Musical acoustics of orchestral water crotales.

An experimental investigation of orchestral crotale vibrational modes in water is presented, along with a qualitative virtual mass model describing the observed effects. Changes in frequency, overtone ratio, and mode splitting as a function of water depth are reported for a C(6) crotale using electronic speckle-pattern interferometry. These data are related to perceived changes in pitch and timbre, along with the creation of audible beats at particular water depths. It is also shown that the suspension method used by musicians when dipping crotales into water leads to the creation of additional acoustically significant modes that are not excited when the crotales are mounted in the standard manner.

Normal modes of a musical drumhead under non-uniform tension.

The effect of non-uniform tension on the normal modes of musical drumheads is examined. Using the standard (m,n) designation for the number of nodal diameters and circles, ideal circular membrane modes with m>0 are doubly degenerate. These degeneracies can be lifted by perturbations to the circular symmetry. Of practical interest to drummers are perturbations caused by non-uniform tension applied at the rim of the drum, leading in some cases to audible frequency splitting. The role of the (1,1) mode in practical drum tuning is analyzed using data obtained using time-averaged electronic speckle-pattern interferometry along with finite element analysis. The resulting model is then generalized to include all modes, using symmetry arguments along with a selection rule taken from group theory. The model compares favorably with both perturbation theory and finite element analysis, and is consistent with experimental observations.