Question

Tuning a guitar string, you play a pure 330 Hz note using a tuning device, and pluck the string. The combined notes produce a beat frequency of 5 Hz. You then play a pure 350 Hz note and pluck the string, finding a beat frequency of 25 Hz. What is the frequency of the string note? Answer:

Tuning a guitar string, you play a pure 330 Hz note using a tuning device, and pluck the string. The combined notes produce a beat frequency of 5 Hz. You then play a pure 350 Hz note and pluck the string, finding a beat frequency of 25 Hz. What is the frequency of the string note?

Answer 1

Beat frequency, fb = |f1 - f2|
Where f1 and f2 are the two frequencies that superimpose to produce the beat frequency fb
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In the first case,
fb = 5 Hz, f1 = 330 Hz, consider the frequency of the string note as f.
|f1 - f| = fb
|330 - f| = 5
f can be either 325 Hz or 335 Hz
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Now consider the second case,
fb = 25 Hz, f1 = 350 Hz
|350 - f| = 25
f can be either 325 Hz or 375 Hz
Considering the previous possible values of f,
f = 325 Hz