Recently, E. G. Richardson (Proc. Phys. Soc., May 1928) by using acoustic impedance methods, has developed a theory of vibration of air cavities which covers the extreme cases of pipes and resonant cavities, and avoids the necessity for a special open-end correction. He obtains the formula tankL=KIkA where K is the conductivity of the neck and A is the area of section of the cavity, assumed cylindrical. This formula leads to the recognised values of N for pipes and resonators.
Double Resonators.—In certain circum stances, where an increased sensitivity is desired, double resonators, consisting, for example, of a resonator of the closed pipe variety combined with one of the Helm holtz type, are usually employed.
By this method, which was first sug gested by Boys, a large increase in ampli tude may, as a rule, be obtained. The theory of such compound resonators was given by Rayleigh, and has been considerably extended recently by E. T. Paris, who uses them in conjunc tion with the hot-wire microphone.
Helmholtz Resonator Combined with Tuned Reed E. Four nier d'Albe has employed a sharply tuned reed (clamped free) with a small mirror attached, to indicate resonance in an air cavity. The resonant vibrations in the air cavity agitate the tuned reed, which lies across the mouth, and cause a spot of light, reflected from the mirror, to oscillate. The combination of reed and air cavity responds to one frequency only, for the overtones of the cavity do not correspond to those of the reed.
The Voice and Speech.—The human voice is an excellent example of a combination of vibrating reeds (the vocal cords) and resonant air cavities (the front and back parts of the mouth, separated by the tongue, and the upper or nasal cavity). The analysis and synthesis of speech sounds was commenced by Helmholtz. More recently Paget has shown that "every series of sung or spoken vowels is in fact a trio performed by three instruments, a reed and two and which the soprano is in close harmonic relation with the reed." In a series of important papers (Proc. Roy. Soc., 1923, 1927) Paget has analysed and synthesised the vowel and con sonant sounds. Observations on breathed vowel sounds indi cated that in every case the oral cavity as a whole, from larynx to lips, actually gives two simul taneous resonances for each vowel sound. In certain cases, more frequent in American cent " a third resonance due to the upper or nasal cavity may be introduced. By means of plas ticine models Paget successfully reproduced the various vowel and more important consonant sounds, as well as combinations of these in well recognised words.
Crandall and Mackenzie (Phys.
Rev., March 1922) have deter mined experimentally the energy distribution in speech as a function of frequency. (See curve fig. 7.) The maximum energy of the male voice occurs at a frequency near 12o p.p.s., the female voice having a maximum about an octave higher. In spite of the fact that the energy of the voice is mostly of low pitch it is the high pitched sounds which are essential to intelligibility of speech. The clearness of speech is unimpaired if all sounds up to 500 frequency are out (6o% of the sound energy being thereby removed). We shall see later that the ear is most sen sitive in the region t,000 to 4,00o frequency. The rate of emission of sound energy in conversational speech has been estimated by Sabine (Phys. Rev., 21, 1923) as 125 ergs/sec and for public speech about 2,500 ergs/sec.
Absorption of Sound by Resonators: Sound Filters.— A well tuned resonator absorbs energy of corresponding frequency from the sound-field in which it is placed. This absorption may extend over an area of the order XV r where X is the wave length of the incident sound (X= c/N). Quincke (1866) employed resonators to stop tones of definite pitch from reaching the ear (see Rayleigh, Sound, vol. ii., p. arrangement acting as a sound-filter. A complex sound passing through a pipe could have any particular tone removed, by fitting a suitable side tube to the pipe. This side tube of length I was closed by a sliding piston which served to "tune" the tube (41= c/N) to any fre quency N it was desired to absorb from the main pipe. Using a succession of such tuned side tubes a corresponding number of tones could be filtered out of the direct sound. G. W. Stewart (Phys. Rev., 1923-26) has greatly extended the possibilities of sound filters by introducing the analogy of electrical filter circuits and the conception of acoustic impedance. On such a basis it is possible to design functioning as and " as in the correspond ing electrical cases. The " filter transmits only those fre quencies below a certain limit, the above a certain limit, and the " only within a certain range or ranges. Filters of this nature are used in the laboratory for purifying sounds, e.g., removing harmonics from a complex wave-form to obtain a pure tone; and in connection with speaking devices.