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Homework answers / question archive / To tune a guitar string to 329 Hz, you compare its frequency with a 329-Hz tuning fork
To tune a guitar string to 329 Hz, you compare its frequency with a 329-Hz tuning fork. Initially, you hear a beat frequency of 5 Hz. Then you slowly tighten the guitar string, which increases its frequency. As a result, the beat frequency decreases steadily to 3 Hz. What are the initial and final frequencies of the guitar string?
The detailed solution is explained below:
Step-by-step explanation
The frequency of the guitar string is inversely proportional to the beat frequency, it is given as the difference of the frequencies, the calculation is shown below:
??f1?−f2??=fbeat??329−f2??=5329−f2?=−5329−f2?=5f2?=334,324??
From the above calculation we can see that two values are possible for the initial frequency, the calculation for the final frequency is shown below:
??f2?−f3??=fbeat??334−f3??=3f3?>334334−f3?=−3f3?=337Hz?334−f3??=3334−f3?=−3f3?=337Hz324−f3?=−3f3?=327Hz??
Thus, we can see that two values of the final frequency is also possible for the given initial frequencies.
(334,337),(324,327)
