A guitar string produces 3 beats/s when sounded with a 350-Hz tuning fork and 8 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.
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This is Giancoli Answers with Mr. Dychko. The first beat frequency fb initial is going to be the frequency of the string minus the frequency of the initial tuning fork that's used. And we're using absolute value here because the beat frequency doesn't tell you whether the string frequency is higher or lower than the tuning fork, we don't really know. So, all we know is that the string frequency minus the tuning fork frequency equals plus or minus the beat frequency. So, the string frequency is going to be plus or minus the initial beat frequency plus the initial frequency of the tuning fork. So, that's plus or minus 3 hertz plus 350 hertz. And so the string frequency is either 353 hertz or it's 347 hertz. And then we compare this string with the second tuning fork, the final tuning fork and we'll find that 347 hertz is a common possibility in the 2 scenarios which makes it the answer. But... Anyway. The string frequency according to the second final tuning fork is the beat frequency in the final case, plus the tuning fork frequency. So, that's plus or minus 8 hertz plus 355. So, 363 or 347 hertz are the possibilities there. And since 347 appears in both scenarios, that is the answer.
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