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With regard to attenuation there is ample evidence confirming the above theory which indicates a rapid decrease of range with increasing frequency. For example in air, for sound-waves of frequency moo, X=33 cms., we find 1=40 kilometres since 2.511= 0-33 for air. The value of 1 at a frequency ioo,000 is consequently 4 metres only. In sea water v = 0.0i3 that is = 0.0325, and c= 1.5 X cms./sec., whence / = 3 .9 X kilo metres at a frequency of i000 (X =15o cms.), and 1=3.9 kilo metres at a frequency of mo,000 (X= i.5 cms.). It is thus evi dent the attenuation of sound-waves in sea water due to viscosity and heat losses is almost negligible compared with the attenuation at corresponding frequencies in air. This accounts to some extent for the relatively large ranges of transmission observed under the sea compared with those in air for the same amount of sound energy at the source. A small charge (9 oz.) of guncotton ex 'G. W. Pierce has shown experimentally that CO, becomes opapic to sound-waves at a frequency of 2X io' p.p.s.

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under water can be detected (and recorded by an Ein thoven galvanometer) at 4o miles (see Wood and Browne, Phys. Soc. Proc., 1923). It is extremely improbable that such a range could be obtained in air. This comparison is of course only of a rough nature, for the wave form and the initial "amplitudes" would not be the same in the two cases. There is ample evidence to show, however, that the attenuation of bell sounds and other noises under water is less than in air. On account of other factors (nature of sound sources, homogeneity of medium, etc.) a strict comparison is somewhat difficult. Attenuation by scattering in a heterogeneous medium may be a serious factor in regard to loss of range in signalling by sound-waves. Tyndall found that a homo

geneous atmosphere, clear or uniformly foggy, transmitted a sound signal to far greater distances than a "patchy" atmosphere containing masses of air at different temperatures, wind eddies, etc. Similarly when sound travels through water it may be seriously interrupted if it meets with a mass of bubbles. The sound of a ship's propeller does not pass very well through the bubbly water in the wake. Air bubbles in the sea may therefore be a serious cause of attenuation, the effects of viscosity and heat conduction being relatively small.

Sound Absorption in Narrow Tubes and Cavities. Porous Bodies.—When sound-waves fall on certain bodies which may be regarded as a mixture of solid and gas, e.g., cork or felt, it is found that a large proportion of the incident energy is absorbed due to viscosity and heat conduction. The influence of these factors is enormously increased on account of the large surface of solid matter in contact with the vibrating gas particles. Viscous forces are increased at the surface of the solid, and the latter serves also as an effective means of reducing the temper ature fluctuations in the compressed gas, i.e., the compressions and rarefactions are no longer adiabatic. Rayleigh has shown theoretically (Sound, Vol. II, p. 331) that the attenuation of sound-waves in a narrow tube of circular section is proportional to the square root of kinematic viscosity 0, and the frequency N, and inversely proportional to the radius of the tube. Porous materials like felt, wool, cork, etc., are effective sound absorbers, and are used to reduce reverberations in auditoriums.