The resulting wave thus has a frequency of (ν 1 + ν 2)/2, the average of the two individual frequencies, and the amplitude factor is now the quantity in brackets, which varies with a frequency of (ν 1 - ν 2)/2. Because of the way cosines add, this can be written: The superposition of the two waves gives the resultant displacement as y = y 1 + y 2 = A (cos 2πν 1 t + cos 2πν 2 t). If we call the frequencies of the two individual waves ν 1 and ν 2, for a particular point we can express the displacements produced by the waves as y 1 = A cos 2πν 1 t and y 2 = A cos 2πν 2 t, respectively (where A = y max). In the wave on the right, there are now five maxima in the same time span in which there were 20 and 15 in the two original waves. If we take the length of the plots as corresponding to one second, then these represent two waves, one of 20 Hz and one of 15 Hz. Below are two sinusoids, the one on top having 20 cycles and the bottom one having 15 cycles. These waves can, of course, be of any shape, and they do not have to be the same amplitude, but the case of two sinusoidal waves of equal amplitude makes a good illustration. The oscilloscope also has an XGA port that connects to the data projector in each lecture hall, so you can easily make the display visible to the whole class.īeats are a phenomenon caused by the superposition of two waves that have slightly different frequencies. To do this, it may be necessary to change the time base setting by one or two steps, but this is quick and easy to do.

The oscilloscope also does a good job of displaying the 1-to-2-Hz beats that occur with the two 266-Hz forks prepared as described above. This is the purpose of the oscilloscope, which in the photograph above is showing the 10-Hz beating between the 256-Hz and 266-Hz tuning forks.

It may be desirable, however, for the students also to have a visual display of what is happening to cause the beats. The main point of this demonstration is for the class to hear the beats. 445), my impression is that these 10-Hz beats are fairly obvious. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), p. Though Resnick and Halliday state that one can detect beats by ear up to a frequency of about seven Hz (Resnick, Robert and Halliday, David. When you strike the 256-Hz tuning fork and then one of the 266-Hz forks, this generates beats at 10 Hz. With the small lumps of clay in the plastic tub, you can vary the beat frequency from about 0.5 Hz to around 10 Hz. When you then strike both of the 266-Hz tuning forks, you hear beats having a frequency equal to the difference in their frequencies. How much lower depends on how much clay you add. When you press a small lump of clay onto one of the tines of one of these tuning forks, the added mass lowers its frequency somewhat. When you sound the two tuning forks that are tuned to 266 Hz, the class hears a pure tone. The idea of this demonstration is to illustrate the beats that occur when one sounds two tones that are close in frequency to each other, but not exactly the same frequency. According to the modern musical standard for an equally-tempered scale in which A = 440 Hz, middle C is 261.63 Hz.) Whichever way you use the demonstration, you must use the hard-wired house microphone, placed near the opening of the resonating box of the middle tuning fork (or, if you use only the two 266-Hz forks, between the openings of their boxes), so that the class can hear the tones. (256 Hz is, by the obsolete “physics standard,” middle C. The three tuning forks in the photograph, from left to right, sound at 256 Hz, 266 Hz and 266 Hz, respectively. You can, of course, perform the demonstration in the original way if you wish. The original page for this demonstration showed two tuning forks, both tuned to 266 Hz, clay and a mallet, and no oscilloscope.

Purpose of tuning fork