Question
Can the average person tell that a 2002-Hz sound has a different frequency than a 1999-Hz sound without playing them simultaneously?
Final Answer
No, it would not be possible to distinguish between these frequencies since their percent difference is only 0.15%, which is less than the minimum of 0.3%.
Solution video
OpenStax College Physics for AP® Courses, Chapter 17, Problem 58 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. The textbook tells us that in order to distinguish between two frequencies, they need to be different by at least 0.3 percent. So the two frequencies are 2002 hertz and 1999 hertz so the question is by what percent difference are they? So the percent difference between those two frequencies is the absolute difference divided by let's say the smaller one times a 100 percent which is 0.15 percent. Now if these frequencies were played at the same time, there would be a beat frequency of 3 hertz and that is something that people could notice and so it would be possible to tell that there's two different frequencies if they were played at the same time but this question says they are played at different times and so beat frequency will not apply. And so they need to differ by at least 0.3 percent but their difference is only 0.15 percent and so it will not be possible to distinguish these frequencies.