# Question Video: Determining the Vibration Frequency Required to Produce a Particular Beat Frequency

The middle C hammer of a piano hits two strings, producing beats of frequency 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?

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### Video Transcript

The middle C hammer of a piano hits two strings, producing beats of frequency 1.50 hertz. One of the strings is tuned to 260.00 hertz. What frequencies could the other string have?

Weβre told in the statement that the beat frequency of the sounds produced by the two strings is 1.50 hertz; weβll call that π sub π΅. Weβre also told that one of the strings is tuned to a frequency of 260.00 hertz; weβll call that π sub one. We want to know what are the possible frequencies of the other string; weβll call those frequencies π sub two.

To begin this problem, letβs recall the relationship for the beat frequency. Created by two overlapping frequencies, a beat frequency, π sub π΅, is created when two nonidentical frequencies interfere with one another. The magnitude of the difference between those two overlapping frequencies is what produces the beat frequency, π sub π΅.

In our case, π sub π΅ equaling the magnitude of π sub one minus π sub two means that there are two possible values for π sub two. To find them, letβs plugin for the given values of π sub π΅ and π sub one. 1.50 hertz equals the magnitude of the difference between 260.00 hertz and π sub two.

So π sub two could either be less than π sub one by 1.50 hertz, which would mean that π sub two is equal to 260.00 hertz minus 1.50 hertz, or π sub two could be greater than π sub one by 1.50 hertz. In this case, π sub two is equal to the sum rather than the difference between π sub one and π sub π΅.

Calculating these values, we find that π sub two can equal 258.50 hertz or it could also equal 261.50 hertz. These are the two possible values of the other string to create a beat frequency of 1.50 hertz.