Harmonic Analysis

gas, tube, noise, vibration, sounds, singing, blades, sound, supply and prism

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Sounds Produced by Rotating Propellers.

The hum of an electric fan which increases in pitch with increase of speed can be heard only at a short distance. The noise produced by the propeller (airscrew) of an aeroplane may, under favourable conditions, be heard several miles away. The sound emitted in both these cases arises, in the absence of excessive vibration, from the rotation of the "source and sink system " associated with the pressure differences on the rotating blades. A. Fage (Roy. Soc. Proc., 107, 1925) has analysed the sounds emitted from various types of airscrews by means of a resonator, of con tinuously variable tuning, fitted with a Tucker hot wire micro phone. He found that the sound of rotation consists of a large number of harmonics having as fundamental a note of frequency equal to the product of the number of blades and the rotational speed. In addition to these sounds, "tearing sounds" associated with the shedding of eddies from the blades were also observed but the frequencies were not determined. Sounds arising from the flexural vibrations of the airscrew blades and the shaft were found to have frequencies in agreement with calculation.

Propellers Under Water.—Most of the under-water noise from a moving ship comes from the screw propeller. As it revolves, "cavitations" are formed just behind the blades. When these cavitations collapse either on themselves or on the blades, a noise is produced. This noise has no predominant frequency, although it is to some extent characterised by the beat of the engines or the rush of the turbines which drive the propeller. If the latter revolves slowly the cavitations are not formed and there is very little noise. With suitable receivers (hydrophones) the noise of a ship proceeding at a moderate speed, say io or 15 knots, can be heard several miles away. (See Bragg, World of Sound.) Explosive Sounds.—The ejection of a shell from a gun and the subsequent explosion of the shell are both accompanied by a pressure-wave of large amplitude which can be detected at long ranges. This pressure-wave has, however. a different character in the two cases—the explosion at the gun is due to the ignition of cordite which burns relatively slowly when compared' with the rate of detonation of the T.N.T. in the shell. Consequently the gun-wave has a wave-front which is much less abrupt than that of the shell detonation. This appears to the ear as the difference between a "boom" and a "crack." An observer of such pressure waves at a distant point receives what appears to be a continuous train of waves, i.e., a reverberation effect, due to the numerous reflected pulses from objects along the track of the primary pulse. Such reverberations may last several seconds. Similar effects are observed under water on the explosion of a mine or a depth charge. The explosion of a few ounces of guncotton under water can be detected and recorded 3o or 4o miles away. A rapid succession of explosions at equal intervals of time may result in a noise of a more or less musical character. This is exemplified in high speed gas or petrol engines, particularly those with several cylinders operating in succession. The note is harsh and the fundamental is accompanied by a long train of harmonics. The musical noise of a high frequency Wehnelt electrolytic inter rupter (used in X-ray work) is also due to a regular succession of explosive impulses, arising from the sudden generation of gas under the liquid. The wave-form of such a series of impulses

recorded on a cathode-ray oscillograph indicates the extremely abrupt nature of detonations. A single impulse is often sufficient to set a resonator into vibration, thereby producing, indirectly, a musical note.

A single impulse of an explosive nature, produced by a power ful electric spark has been employed in the study of the progress of a sound-wave under controlled conditions—particularly in connection with the complex reflections of sound-waves in audito riums. (See ACOUSTICS OF BUILDINGS.) Sounds Maintained by Heat.—Most bodies on being heated will expand and in so doing perform a certain amount of mechan ical work. If the phases of the forces thus called into play are favourable, a vibration may be set up and maintained.

Trevelyan's rocker is a good example of such a maintained vibration. It consists of a prism of brass or copper almost tri angular in section with one edge grooved to form two adjacent parallel ridges. The prism rests with its groove downwards on a block of lead with a rounded top, the end of the prism terminat ing in a ball which rests on a smooth surface. When the prism is heated and placed on the lead block it begins to vibrate, the weight being carried alternately on one or the other of the two ridges. The cause of these vibrations was ascribed by Leslie to the expansion of the cold block at the point of contact with the hot metal. The effect can be obtained also by a local heating of the points of contact by means of an electric current.

Singing Flames.—Under certain circumstances a small gas flame inserted into a resonant chamber of air or other gas, will emit a musical sound. If heat be given to the air in a vibrating column at the instant of greatest condensation the vibration will be encouraged. If the phase of the heat supply be reversed the vibration will be discouraged. An essential feature of the main tenance of the vibration is the presence of stationary waves in the gas supply tube as well as in the singing tube. The jet must be a node to correspond with a node in the singing tube where the maximum pressure-amplitude occurs. For most satis factory operation therefore it is necessary (a) that the gas jet should be at or near a node in the singing tube and (b) that the length of the gas supply tube should be an odd multiple of X/4 (where X is the wave-length, in the gas, of the note sounded). The tube will not sing at all if the length of the supply tube lies between X/4 and X/2, 3X/4 and X, and so on. Spherical resona tors, large globes, may also be employed, and bulbous chimneys as used for paraffin lamps give satisfactory results. The inter mittent character of a singing flame is easily demonstrated by means of a revolving mirror, from which it appears that at one phase the flame may withdraw itself entirely within the gas supply tube. The vibrations sometimes reach sufficient intensity to extinguish the flame completely. For a complete discussion of the phenomena of singing flames Rayleigh's Sound, vol. ii., p. 224, should be consulted.

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