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Explanation of beat frequencies in sound - Succeed in Physical Science. Also refer to physics, waveform, vibration, compression, transverse, sine wave, units, wavelength, frequency, amplitude, volume, pitch, tone, velocity, speed, Ron Kurtus, School for Champions. Copyright © Restrictions Beat Frequencies in Soundby Ron Kurtus (revised 7 December 2007) The sound of a beat frequency or beat wave is a fluctuating volume caused when you add two sound waves of slightly different frequencies together. If the frequencies of the sound waves are close enough together, you can hear a relatively slow variation in the volume of the sound. A good example of this can be heard using two tuning forks that are a few frequencies apart. A sound wave can be represented as a sine waves, and you can add sine waves of different frequencies to get a graphical representation of the waveform. When the frequencies are close together, they are enclosed in a beat envelope that modulates the amplitude or loudness of the sound. The frequency of this beat is the absolute difference of the two original frequencies. Questions you may have include:
This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Useful tools: Metric-English Conversion | Scientific Calculator. Examples and applications of beat frequenciesA good demonstration of beat frequencies can be heard in the animation below. A pure sound of 330 Hz is combined with 331 Hz to give a rather slow beat frequency of 1 Hz or 1 fluctuation in amplitude per second. When the 330 Hz sound is combined with a 340 Hz sound, you can hear the more rapid fluctuation at 10 Hz. Click on the buttons below to hear the pure tone and the different beat frequencies.
Another exampleWhen you fly in a passenger plane, you may often hear a fluctuating droning sound. That is a beat frequency caused by engine vibrations at two close frequencies. Application of beatsA piano tuner will strike a key and then compare the note with a tuning fork. If the piano is slightly out of tune, he will be able to hear the beat frequency and then adjust the piano wire until it is at the same frequency as the tuning fork. If the piano is severely out of tune, it makes the job more difficult, because the beat frequency may be too fast to readily hear. Adding sine wavesAlthough sound is a compression wave that travels through matter, it is more convenient to illustrate the sound wave as a transverse wave, similar to how a guitar string vibrates or how a water wave appears. The shape of such a wave for a single frequency is called a sine wave.
Sine wave representing a single frequency of sound with constant amplitude When you add sound waves traveling in the same direction together, elements of the sine wave add or subtract, according to where they are in the waveform. You add the amplitude of each wave, point-by-point. Making a graphical representation of the sum of two waves can be done by hand, but that can be be tedious. Usually, it is done mathematically. Beat envelopeIf you add two waves of slightly different frequencies, the resulting amplitude will vary or oscillate at a rate that is the difference between the frequencies. That beat frequency will create a beat envelope around the original sine wave.
Beat envelope modulates the amplitude of the sound Since the frequencies of the two sounds are so close, you would hear a sound that is an average of the two. But you would also hear the modulation of the amplitude as a beat frequency, which is the difference between the initial frequencies: fb = | f1 − f2 | where
ExamplesFor example, if you add a wave oscillating at 445 Hz with one that is at 450 Hz, the resulting frequency will be an average of the sum of the two waves: (445 Hz + 450 Hz)/2 = 447.5 Hz. This waveform is close to a sine wave, since the frequencies are almost the same. The amplitude of volume of this combination will oscillate at the beat frequency of the difference between the two: (450 Hz - 445 Hz) = 5 Hz. Now, if you add 440 Hz and 500 Hz notes, the resulting waveform will be a complex version of a sine wave and will sound like a blurred or fuzzy average of the two tones. The average frequency of this complex wave will be (440 Hz + 500 Hz)/2 = 470 Hz. Also, its beat frequency will be 60 Hz, which would sound like a very low-pitched hum instead of a fluctuating volume. SummaryA beat frequency is the combination of two frequencies that are very close to each other. The sound you hear will fluctuate in volume according to the difference in their frequencies. You may often hear beat frequencies when objects vibrate. Beat frequencies can be graphically shown by adding two sine waves of different frequencies. The resulting waveform is a sine wave that has an envelope of modulating amplitude. Always do your best ResourcesThe following resources provide information on this subject: WebsitesBeats - Hyperphysics Books
Top-rated books on the Physics of Music MiscellaneousMini-quiz to check your understanding1. How could you tell that two tuning forks of the same musical note, were exactly the same? 2. If you added two sine waves that are exactly the same, what would be the result? 3. What would the beat frequency be if you added tones of 880 Hz and 882 Hz? If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again. What do you think?Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible. Share linkFeel free to establish a link from your website to pages in this site. 
Or use our form to send this link to yourself or a friend. Students and researchersThe Web address of this page is Please include it as a reference in your report, document, or thesis. Where can you go from here?
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