The greatest effect of air loading on the vibration of the cone occurs when there are large changes in pressure over the surface of the cone. The maximum change in pressure will be at Helmholtz resonant frequencies and therefore the corresponding mode shapes are studied. By applying the methods to an axisymmetric loudspeaker, the Helmholtz properties may be examined whilst reducing the dimension of the problem by one and thus reducing the computational expense when compared to the full three-dimensional analysis that is necessary for a general loudspeaker design. In addition, considerable previous work has been done on the structural vibration of axially symmetric loudspeaker drive units (see Jones  and Jones and Henwood , for example). In this work we show results for the cabinet shown in Figure 6.1, which is basically a cylinder 120mm deep and 132mm in diameter. The loudspeaker has a conical drive unit of radius 80mm fitted. Given these dimensions, the lowest cabinet resonance occurs around 1kHz, and the cabinet resonances can be observed in sound pressure measurements outside the cabinet.
For the measurement of the resonant frequencies, microphone readings of the sound pressure were taken at various positions within the cabinet. Measurements were made through all frequencies of interest, commencing at 20Hz and going through to 20kHz. The peaks in the response inform us of the internal resonant frequencies.
|Table 6.B: Computed and measured loudspeaker resonant frequencies
||Mode || Boundary Element || Experimental
||1 || 1414 Hz || 1318 Hz
||2 || 1590 Hz || 1679 Hz
||3 || 2232 Hz || 2133 Hz
||4 || 2815 Hz || 2691 Hz
||5 || 2876 Hz || 3306 Hz |
The major contribution to the discrepancy between the measured and calculated values is believed to be the simplicity of the model chosen, which fails to include any internal structure to the loudspeaker. In addition, the maximum pressure occurs at slightly different frequencies for different microphone positions.
Figure 6.2 shows the first, third and fifth mode shapes obtained via the boundary element method. The mode shapes are constructed from the returned values of f* in the domain. The values on the contours are arbitrary.