The bowl’s trapped air shifts kettledrum mode frequencies from ideal values.

Evidence

The modes produced when a kettledrum is struck are the same shape as those given in Figure 4.31, but their mode frequencies are different from those of an unmounted head (shown as “ideal” in Table 4.2), because of the effect of the air in the bowl over which the head is stretched and the position at which it is struck. Hall (2001) describes this as follows: “When sections of the head move into and out of the bowl, other sections move in the opposite direction (out of and into the bowl respectively).” These are marked in Figure 4.31 with plus and minus signs. The (0,1) mode is an exception to this, and it is marked with “−/+” since it involves the whole head moving either into or out of the bowl, as it attempts to compress and rarefy the trapped air respectively. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1302

Categorization

Category: Causal Relationships

• QUESTION: How much do the mode frequencies shift relative to the ideal, and does the vent hole fully restore ideal behavior?

Related

• Trapped air in a drum bowl alters the head’s mode frequencies from ideal values (similarity 0.83)
• The kettledrum bowl lowers its head modes toward harmonic ratios (similarity 0.82)
• Kettledrum tone quality depends on strike position relative to nodal rings (similarity 0.80)