# Modal interaction

The following shows an examplel of modal interactions for a 20 kHz $$\phi$$40 mm horn ($$c_{tw}$$ = 5100 m/sec; Poisson's ratio = 0.33). The horn length was tuned as needed to maintain the axial resonance (the maximum adjustment was 0.1 mm). Also see Amplitude asymmetry. Figure 1. Frequencies for a 20 kHz $$\phi$$40 mm horn Figure 2. Face amplitude asymmetries for a 20 kHz $$\phi$$40 mm horn

The following table shows some data from the above graphs. Note how quickly the axial mode asymmetry changes for small changes in the horn diameter and as the axial and nonaxial resonances converge. Also note how the nonaxial modeshape changes as it interacts with the axial mode.

Table notes —

1. All displacements (as represented by the image colors) are in the axial direction.
2. All displacements are displayed at the same scale.

Diameter (mm) Frequency
separation (Hz)
Axial mode Nonaxial mode
38.00 -265 20005 Hz Asymmetry = 0.001 19740 Hz
39.00 -27 20000 Hz Asymmetry = 0.06 19973 Hz
39.02 -18 19998 Hz Asymmetry = 0.34 19982 Hz
39.05 -12 20000 Hz Asymmetry = 0.50 19988 Hz
39.10 6 20000 Hz Asymmetry = 0.96 20006 Hz
39.20 27 20000 Hz Asymmetry = 0.18 20027 Hz
39.30 42 20001 Hz Asymmetry = 0.06 20043 Hz
41.00 424 19996 Hz Asymmetry = 0.008 20420 Hz