Beats
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-209
2025-11-16
29
When two sounding bodies that have nearly the same time of vibration are sounded together, the alternate interference and coincidence of the sound waves produce rhythmical variations in the intensity of the sound. These are called beats and can be readily heard.
If the waves sent out by the two sources are represented by the curves in the upper part of Fig. 1, we can see that one body must vibrate ten times while the other vibrates eleven. This means
that at every tenth wave of one, and every eleventh wave of the other, the waves will interfere, while at times midway between the waves will assist each other. The curve resulting from these two sets of waves is shown in the heavy line. The beat would come between F and G, at that part of the curve which swings the greatest distance from the straight-line AB, while at A or B, where the interference is nearly complete, there would be very little sound. The heavy curve is constructed as follows: draw a set of vertical lines across the straight-line AB; then any point e on the curve will be found by making de equal to the sum or difference of ab and ac, depending upon whether they are upon the same or opposite sides of AB. It is evident that in order to make a curve that will represent several beats between two musical sounds, a much more extended drawing would be required.If two tuning forks, giving 128 and 129 vibrations per second respectively, are sounded together, they will be in the same phase once per second and in opposite phases a half second later. This combination gives one beat per second. If a fork giving 130 vibrations is sounded with the one giving 128, they will be in the same phase twice per second and in opposite phases a quarter second later, and there will be two beats per second. By vibrating together forks with greater differences in the number of their vibrations, it is seen that the number of beats between two sounds is equal to the difference between the numbers of their vibrations per second. This can be demonstrated by the use of two forks that vibrate in the same time. By pre
will be heard when the forks are, sounded together. By increasing the load, pressing a shot into the wax if needed, a greater number of beats per second will be produced.
ssing a piece of beeswax upon one prong of one of these forks, it can be made to give fewer vibrations, and a beat
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