It is well known that persons especially male persons-like to sing in their baths. The usual physicists’ comment on this is that a bathroom, having little soft furnishing, is highly reverberant and gives a weak voice more volume.

 

A room of concert-hall size has dimensions so large compared with sound wavelengths in the voice range that, in this range, adjacent resonant frequencies overlap that is, the fractional difference in frequency is much less than the reciprocal of the ‘quality factor’, 1/Q which states the fractional width of an individual resonant response curve. Such a large room will therefore, if the various resonances all have essentially the same amplitude, not selectively respond to any particular frequencies; that is, it will be ‘reverberant’ but not ‘resonant.’ However, a small room of the size of a typical home bathroom has numerous but discrete resonances within the frequency range of the normal voice; and in such a room the voice will tend to be pulled into synchronism with one or the other of these.

This article argues that a good room for singing in should be so designed that all its resonant frequencies-as nearly as possible- coincide with notes of the musical scale. This article reports a computer study to determine the optimum dimensions for such a room. The room is treated as being essentially a rectangular box with sides A, B, and C metres. The resonant frequencies of such a box are members of three infinite series, viz:

F = N * (343/(2*W)) Hz
where
W = A, B, or C
N = any integer from 1 upwards (and 343 being the velocity in metres per 1 second, of sound in air at normal room temperature).

It is assumed for the purpose of this analysis that the male voice, for instance, does not aim to sing any note above the octave of middle C on the standard chromatic scale (with A4 equal to 44oHz), this note (C5) having a frequency of 523.2Hz. For the purposes of compiling the Tables for this article, a computer program was constructed to:

1) Find all distinct values of W for which all resonances up to 53oHz are within 1 percent of one of the semitones of this chromatic scale (except for the 7th harmonics, which are allowed to be 2 percent out). This is accomplished by testing W-values successively from 1.5 to 4.0 metres, in steps of 0.01 metres. Of several successive W-values which match to one set of semitones, that one is chosen for which the variance of all the resonances from the respective nearest semitone is least; and a table is compiled showing, for each such W-value, the individual deviations throughout the top two octaves, from the C below middle C (C3, with a frequency of 130Hz) to the C above (C5, with a frequency of 523Hz). However, the match is checked, and the variance computed, down to 41.25Hz, which is the fundamental resonance for the maximum value of W, 4.0 metres).