Question
What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?
Final Answer
Three beat frequencies will be observed: , , and .
Solution video
OpenStax College Physics for AP® Courses, Chapter 17, Problem 40 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. When hitting three different piano strings with three different frequencies, we'll have beat frequencies corresponding to each pair of frequencies we can make from those combinations. So frequency 1 paired with frequency 2 will make a beat frequency of 0.3 hertz when we take the absolute value of f 1 minus f 2 which is 127.8 minus 128.1 hertz. And f 1 paired with f 3 will produce another beat frequency which is 0.5 hertz and then pairing f 2 with f 3 will result in a beat frequency of 0.2 hertz and that's all the combinations you can have with three different things taken two at a time.