The motion of a sound wave must not, however, be confounded with the motion of the molecules which at any moment form the wave; for during its passage every molecule concerned in its transference makes only a small excursion to and fro, the length of the excursion being the amplitude of vibration, on which the intensity of the sound depends.
Taking the same tuning fork mentioned above, the molecule would take 1/256 of a second to make a full vibration, which is the length of time it takes for the pulse to travel the length of the sound wave.
For different intensities, the amplitude of vibration of the molecule is roughly 1/50 to 1/1000000 of an inch. That is to say, in the case of the same tuning fork, the molecules it causes to vibrate must either travel a distance of 1/56 or 1/1000000 of an inch forward and back in the 1/256 of a second or in one direction in the 1/512 of a second.
I might further state that the pitch of the sound depends on the number of vibrations and the intensity, as already indicated by the amplitude of stroke—the timbre or quality of the sound depending upon factors which will be clearly set forth as we advance.
Having now clearly and correctly represented the wave theory of sound, without touching the physiological effect perceived by means of the ear, we will proceed to consider it.
We must first consider the state in which the supposed molecules exist in the air, before making progress.
The present science teaches that the diameter of the supposed molecules of the air is about 1/250000000 of an inch (Tait); that the distance between the molecules is about 8/100000 of an inch; that the velocity of the molecules is about 1,512 feet a second at O°C., in its free path; that the number of molecules in a cubic inch at O°C. is 3,505,519,800,000,000,000 or 35 followed by 17 ciphers (35)17; and that the number of collisions per second that the molecules make is, according to Boltzmann, for hydrogen, 17,700,000,000, that is to say, a hydrogen molecule in one second has its course wholly changed over seventeen billion times. Assuming seventeen billion or million to be right for the supposed air molecules, we have a very interesting problem to consider.
The wave theory of sound requires, if we expect to hear sound by means of a C3 fork of 256 vibrations, that the molecules of the air composing the sound wave must not be interfered with in such a way as to prevent them from traveling a distance of at least 1/50 to 1/1000000 of an inch forward and back in the 1/256 of a second. The problem we have to explain is, how a molecule traveling at the rate of 1,512 feet a second through a mean path of 8/100000 of an inch, and colliding seventeen billion or million times a second, can, by the vibration of the C3 fork, be made to vibrate so as to have a pendulous motion for 1/256 of a second and vibrate through a distance of 1/50 to the 1/1000000 of an inch without being changed or mar its harmonic motion.
It is claimed that the range of sound lies between 16 vibrations and 30,000 (about); in such extreme cases the molecules would require 1/16 and 1/30000 of a second to perform the same journey.
It must not be forgotten that a mass moving through a given distance has the power of doing work, and the amount of energy it will exercise will depend on its velocity. Now, a molecule of oxygen or nitrogen, according to modern science, is a mass 1/250000000 of an inch in diameter, and an oxygen molecule has been calculated to weigh 0.0000000054044 ounce. Taking this weight traveling with a velocity of 1,512 feet a second through an average distance of 8/100000 of an inch, the battering power or momentum it would have can be shown to be in round numbers capable of moving 1/200000 of an ounce.