Beats Can Be Heard When Two Tuning Forks

The original page for this demonstration showed two tuning forks, both tuned to 266 Hz, clay and a mallet, and no oscilloscope. You tin can, of grade, perform the demonstration in the original way if y'all wish. The iii tuning forks in the photograph, from left to right, sound at 256 Hz, 266 Hz and 266 Hz, respectively. (256 Hz is, past the obsolete "physics standard," centre C. According to the mod musical standard for an equally-tempered calibration in which A = 440 Hz, middle C is 261.63 Hz.) Whichever style you use the demonstration, you must use the hard-wired business firm microphone, placed near the opening of the resonating box of the middle tuning fork (or, if you utilise only the two 266-Hz forks, between the openings of their boxes), so that the class tin can hear the tones.

The idea of this demonstration is to illustrate the beats that occur when i sounds ii tones that are close in frequency to each other, only not exactly the aforementioned frequency. When you sound the ii tuning forks that are tuned to 266 Hz, the grade hears a pure tone. When you printing a small lump of clay onto 1 of the tines of ane of these tuning forks, the added mass lowers its frequency somewhat. How much lower depends on how much clay you add. When you and then strike both of the 266-Hz tuning forks, you hear beats having a frequency equal to the divergence in their frequencies. With the small lumps of clay in the plastic tub, yous tin vary the trounce frequency from almost 0.5 Hz to around ten Hz.

When you strike the 256-Hz tuning fork and so one of the 266-Hz forks, this generates beats at ten Hz. Though Resnick and Halliday state that one can observe beats by ear up to a frequency of about vii Hz (Resnick, Robert and Halliday, David. Physics, Part Ane, Tertiary Edition (New York: John Wiley and Sons, 1977), p. 445), my impression is that these ten-Hz beats are adequately obvious.

The main indicate of this demonstration is for the grade to hear the beats. It may be desirable, notwithstanding, for the students also to accept a visual brandish of what is happening to cause the beats. This is the purpose of the oscilloscope, which in the photograph in a higher place is showing the 10-Hz chirapsia betwixt the 256-Hz and 266-Hz tuning forks. The oscilloscope also does a good job of displaying the ane-to-two-Hz beats that occur with the ii 266-Hz forks prepared as described above. To do this, it may exist necessary to change the time base setting by one or two steps, but this is quick and easy to do. The oscilloscope besides has an XGA port that connects to the information projector in each lecture hall, so you lot can easily make the display visible to the whole form.

What is happening:

Beats are a phenomenon acquired by the superposition of two waves that have slightly unlike frequencies. These waves tin, of grade, be of any shape, and they do non accept to exist the aforementioned amplitude, simply the case of two sinusoidal waves of equal amplitude makes a good illustration. Below are two sinusoids, the one on acme having xx cycles and the bottom one having 15 cycles. If we take the length of the plots as corresponding to ane 2d, then these stand for two waves, one of 20 Hz and one of 15 Hz.

Below, at left are the two waves superimposed on each other. Yous can see that because of their different frequencies, at some points they are in stage, and at some points they are out of phase. The graph on the correct is the sum of the two waves, with dashed lines showing the envelope of the resulting moving ridge. The peaks, of course, correspond to places where the waves are in stage, and the nodes occur where they are out of stage.

In the wave on the right, at that place are now five maxima in the same fourth dimension span in which there were 20 and 15 in the 2 original waves. If we call the frequencies of the 2 individual waves ν ₁ and ν ₂ , for a particular betoken nosotros tin express the displacements produced by the waves as y ₁ = A cos 2πν _one t and y ₂ = A cos 2πν _ii t, respectively (where A = y _max ). The superposition of the two waves gives the resultant displacement as y = y _one + y ₂ = A (cos 2πν ₁ t + cos 2πν ₂ t). Because of the way cosines add, this can be written:

The resulting wave thus has a frequency of (ν ₁ + ν ₂ )/2, the boilerplate of the 2 individual frequencies, and the aamplitude factor is at present the quantity in brackets, which varies with a frequency of (ν _i - ν ₂ )/2. A maximum in aamplitude occurs whenever cos 2 π((ν _i - ν ₂ )/two)t = one or -1. Since each of these values occurs once per cycle, the beat frequency is twice the term in parentheses, or ν ₁ - ν ₂ , the departure between the frequencies of the two individual waves. Hence the 5-Hz crush in the example higher up for the sum of a xx-Hz wave and a 15-Hz wave.

If the frequencies of two waves are far apart, their sum merely results in a complex waveform, in which the higher-frequency component "rides on" the lower-frequency one. If the frequencies are close, but both relatively loftier, the beats can occur at loftier frequencies. The production of sound-frequency beats from ii radio-frequency oscillations is the basis of an electronic instrument called the theremin.

References:

i) Berg, Richard E. and Stork, David G. The Physics of Audio (Englewood Cliffs: Prentice-Hall, Inc., 1982), pp. 223, 228.
two) Resnick, Robert and Halliday, David. Physics, Role One, 3rd Edition (New York: John Wiley and Sons, 1977), pp. 419-420, 444-445.

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Source: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/44.51.html

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