Project Title
Beat Frequency
Sounds and Exploration
by Peter Rapp '99 (7/20/99)

    When two slightly different frequencies of sound combine, they form a signal with a series of audible "beats." This page will tell you why these "beats" emerge, and how we can predict the beat frequency. (How many beats we hear per second)

     We have already talked about constructive and destructive interference, so you should already have a feel for how this works. Look and listen to the two sounds below. Can you hear a difference? Don't worry if you can't; we can't all be musicians! Let's say you were trying to tune a piano however. You need to know whether or not the frequencies match...

Graph of Frequency 1

This first sound represents what the piano tuner hears when he strikes a tuning fork that he knows to be 300Hz. Next, he plucks the string in question...

Graph of Frequency 2

It may sound about the same, but when both the string and the tuning fork are oscillating, the two sounds combine to produce an interference pattern...

Graph of Interference pattern

     Listen carefully to the combined sound. What do you hear? You should sense a series of beats, 3 per second to be exact. This is called the beat frequency, which is caused by the interference of the two sounds. You should count 3 "beats" per second. There is a simple way to predict the beat frequency if you know the two source frequencies.

     This may seem simple, but just subtract the two source frequencies, and that will be the beat frequency. Since negative values do not make sense, they are adjusted to positive values. If we know two of the terms can we get the third? Sometimes.

     We know that the ??? value could either be 303Hz or 297Hz. How does the piano tuner adjust the string. If he tunes it in the wrong direction by either tightening or loosening the string, he would hear even more beats per second, so he knows he should go the other way. For the curious, the two actual frequencies were 300Hz and 297Hz.

Resources Window
All graphs made with Graphing Calculator, which is included with any Macintosh System Software package since MacOS 8.
Text versions of the equation work are made with Microsoft Equation Editor and are embedded in Microsoft Word documents.
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