According to theory, the velocities of sound in oxygen and hydrogen are inversely proportional to the square roots of the densities of the two gases. We here find this theoretic deduction verified by experiment. Oxygen being sixteen times heavier than hydrogen, the velocity of sound in the latter gas ought, according to the above law, to be four times its velocity in the former; hence, the velocity in oxygen being 1,040, in hydrogen calculation would make it 4,160. Experiment, we see, makes it 4,164.
The velocity of sound in liquids may be determined theoretically, as Newton determined its velocity in air; for the density of a liquid is easily determined, and its elasticity can be measured by subjecting it to compression. In the case of water, the calculated and the observed velocities agree so closely as to prove that the changes of temperature produced by a sound-wave in water have no sensible influence upon the velocity. In a series of memorable experiments in the Lake of Geneva, MM. Colladon and Sturm determined the velocity of sound through water, and made it 4,708 feet a second. By a mode of experiment which you will subsequently be able to comprehend, the late M. Wertheim determined the velocity through various liquids, and in the following table I have collected his results:
Transmission of Sound through Liquids
| Name of Liquid | Temperature | Velocity | |
| River-water (Seine) | 15° C. | 4,714 | feet |
| River”water (S” | 30 | 5,013 | ” |
| River”water (S” | 60 | 5,657 | ” |
| Sea-water (artificial) | 20 | 4,768 | ” |
| Solution of common salt | 18 | 5,132 | ” |
| Solution of sulphate of soda | 20 | 5,194 | ” |
| Solution of carbonate of soda | 22 | 5,230 | ” |
| Solution of nitrate of soda | 21 | 5,477 | ” |
| Solution of chloride of calcium | 23 | 6,493 | ” |
| Common alcohol | 20 | 4,218 | ” |
| Absolute alcohol | 23 | 3,804 | ” |
| Spirits of turpentine | 24 | 3,976 | ” |
| Sulphuric ether | 0 | 3,801 | ” |
We learn from this table that sound travels with different velocities through different liquids; that a salt dissolved in water augments the velocity, and that the salt which produces the greatest augmentation is chloride of calcium. The experiments also teach us that in water, as in air, the velocity augments with the temperature. At a temperature of 15° C., for example, the velocity in Seine water is 4,714 feet, at 30° it is 5,013 feet, and at 60° 5,657 feet a second.
I have said that from the compressibility of a liquid, determined by proper measurements, the velocity of sound through the liquid may be deduced. Conversely, from the velocity of sound in a liquid, the compressibility of the liquid may be deduced. Wertheim compared a series of compressibilities deduced from his experiments on sound with a similar series obtained directly by M. Grassi. The agreement of both, exhibited in the following table, is a strong confirmation of the accuracy of the method pursued by Wertheim:
| Cubic compressibility | ||
| ╭———————^———————╮ | ||
| from Wertheim’s velocity of sound | from the direct experiments of M. Grassi | |
| Sea-water | 0·0000467 | 0·0000436 |
| Solution of common salt | 0·0000349 | 0·0000321 |
| ” carbonate of soda | 0·0000337 | 0·0000297 |
| ” nitrate of soda | 0·0000301 | 0·0000295 |
| Absolute alcohol | 0·0000947 | 0·0000991 |
| Sulphuric ether | 0·0001002 | 0·0001110 |
The greater the resistance which a liquid offers to compression, the more promptly and forcibly will it return to its original volume after it has been compressed. The less the compressibility, therefore, the greater is the elasticity, and consequently, other things being equal, the greater the velocity of sound through the liquid.
We have now to examine the transmission of sound through solids. Here, as a general rule, the elasticity, as compared with the density, is greater than in liquids, and consequently the propagation of sound is more rapid.
In the following table the velocity of sound through various metals, as determined by Wertheim, is recorded:
Velocity of Sound through Metals
| Name of Metal | At 20° C. | At 100° C. | At 200° C. |
| Lead | 4,030 | 3,951 | … … |
| Gold | 5,717 | 5,640 |
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