40 HAND-BOOK OF ACOUSTICS.
To find the wave length of any sound, therefore, it is only necessary to divide the velocity of sound by the vibration number of the sound in question. It -will be noticed that as the velocity of sound varies with the temperature of the air, so the wave length of any particular sound must vary with the temperature.
"We have seen that the pitch of any sound depends ultimately upon the rapidity with which the sound waves strike the tympanum of the ear, and usually this corresponds with the rate of vibration of the sounding body. If, however, from any cause, more sound waves from the sounding body, strike the ear, in a given time, than are emitted from it during that time, the apparent pitch of the note will be correspondingly raised, and vice versa. Such a case occurs when the sounding body is moving towards or from us, or when we are advancing or receding from the sounding body. "When, for example, a locomotive, with the whistle sounding, is advancing rapidly towards the observer, the pitch will appear perceptibly sharper than after it has passed. This fact may be easily illustrated by fastening a whistle in one end of a piece of india-rubber tubing 4 or 5 feet long, and blowing through the other ; at the same time whirling the tube in a horizontal circle above the head. A person at a distance will perceive a rise in pitch as the whistle is advancing towards him and a fall as it recedes.
The lowest sound used in music, is found in the lowest note of the largest modern organs, and is produced by vibrations per
second ; but so little of musical character does it possess, that it is never used except with its higher octaves. The musical character continues to be very imperfect for some distance above this limit; in fact, until we get to above twice this number of vibrations per second. The highest limit of musical pitch at the present time is about 04, a sound corresponding to about 4,000 vibrations per second. Very much higher sounds than this can be heard, but they are too shrill to be of any use in music. Fig. 28, which, explains itself, shows the limits of pitch of the chief musical instruments.
The note C in the treble staff is the sound that musicians usually take as a basis of pitch; this, once fixed, all the other sounds of the musical scale are readily determined. But, unfortunately, at the present day, there are a very large number of vibration numbers, corresponding to this note ; in other words,, there is no universally recognised standard. It appears from Mr. Ellis's paper on "The History of Musical Pitch" that the vibration number