Video: Beats and Beat Frequency

A piano tuner hears a beat every 1.00 s when listening to a 164-Hertz frequency tuning fork and a single piano string. What is the frequency of the string if it is of a lower frequency than the tuning fork?

01:16

Video Transcript

A piano tuner hears a beat every 1.00 seconds when listening to a 164-hertz frequency tuning fork and a single piano string. What is the frequency of the string if it is of a lower frequency than the tuning fork?

In this scenario, the tuner is hearing a beat every 1.00 seconds. That means the beat has a frequency of 1.00 hertz. We can recall that beat frequency, ๐‘“ sub ๐ต, is equal to the difference between the frequency of the one tone being mixed and the frequency of the other tone. And in case ๐‘“ two is greater than ๐‘“ one, we put absolute value bars around this difference. Since the tuner in our example hears a beat every 1.00 seconds, that means thereโ€™s one complete wave cycle each second, or that this beat frequency is 1.00 hertz.

By our beat frequency equation, we can say that this is equal to 164 hertz, the frequency of the tuning fork, minus the frequency of the piano string, which weโ€™ve called ๐‘“ sub ๐‘ . Rearranging, we can say that ๐‘“ sub ๐‘  is equal to 164 minus 1.00 hertz, or 163 hertz. Thatโ€™s the frequency of this piano string before itโ€™s tuned to the tuning fork.

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