Question
The middle-C hammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?
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Solution video
OpenStax College Physics, Chapter 16, Problem 58 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. The hammer in a piano hits two strings producing a beat frequency together of 1.50 hertz. One of the strings we are told has a frequency of 260 hertz and we'll call that f 1. We know the beat frequency is the magnitude of this difference between the two frequencies between the two strings which is to say that f 1 minus f 2 equals either the positive of the beat frequency or f 1 minus f 2 could also be the negative of the beat frequency. So we can solve for f 2 in each case and that gives us the two possibilities for its frequency. So if we have f 1 minus f 2 equals the positive of the beat frequency, we can add f 2 to both sides and then subtract the beat frequency from both sides and then the right hand side, we get f 2 and on the left hand side, we get f 1 minus f b and then we switch the sides around. So we have f 2 equals f 1 minus f b so that's 260.00 hertz minus 1.50 hertz which is 258.50 hertz. Or f 1 minus f 2 is the negative of the beat frequency and so we add f 2 to both sides and then add the f b to both sides to solve for f 2. So f 2 is f 1 plus the f b; 260.00 hertz plus 1.50 hertz which is 261.50 hertz.