The 65.5-cm-long string of a guitar has a fundamental frequency of 374 Hz when i

Question

The 65.5-cm-long string of a guitar has a fundamental frequency of 374 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. If the string is pressed down at this fret and plucked, what is the new fundamental frequency? Hz 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? Hz

Explanation / Answer

We know that fundamental frequency, f = v/2L, where v is the velocity and L is the length.

=> 374 = v/2*0.655 => v = 489.94m/s

a) Now, L'=(2/3)L = (2/3)*0.655 = 0.4366m

Therefore, new fundamental frequency, f = 489.94/2*0.4366 = 561.02Hz

b) The guitarist plucks the string midway between the bridge and the fret. Hence we have to calculate the frequency of second harmonic i.e f'= 2f = 2*561 = 1122 Hz

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