The 63.5-cm-long string of a guitar has a fundamental frequency of 370 Hz when i

Question

The 63.5-cm-long string of a guitar has a fundamental frequency of 370 Hz when it vibrates freely along its entire length. A fret is provided for limiting vibration to just the lower two-thirds of the string.

(a) If the string is pressed down at this fret and plucked, what is the new fundamental frequency?

(b) The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one-sixth of its length from the bridge. What frequency will be heard then? In this case, the location where the string was plucked would be an antinode

Explanation / Answer

  By f = v/2L
=>370 = v/(2 x 0.635)
=>v = 469.9 m/s

(a) Now L = 2/3L = 2/3 x 0.635 = 0.42333 m
Thus by f = v/2L = 469.9/(2 x 0.42333) = 555 Hz

(b) natural harmonic = 2f = 1110 Hz

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