10) The top string of a guitar has a fundamental frequency of340 Hz when it is a

Question

10) The top string of a guitar has a fundamental frequency of340 Hz when it is allowed to vibrate as awhole, along all its 60.0 cm length fromthe neck to the bridge. A fret is provided for limiting vibrationto just the lower two thirds of the string. (a) If the string is pressed down at this fretand plucked, what is the new fundemental frenquency?
Hz
(b) The guitarist can play a "natural harmonic" by gently touchingthe string at the location of this fret and plucking the string atabout one sixth of the way along its length ftom the bridge. Whatfrequency will be heard then?

Hz (a) If the string is pressed down at this fretand plucked, what is the new fundemental frenquency?
Hz
(b) The guitarist can play a "natural harmonic" by gently touchingthe string at the location of this fret and plucking the string atabout one sixth of the way along its length ftom the bridge. Whatfrequency will be heard then?

Hz

Explanation / Answer

(a) fund freq is inversely proportional to length, so weget .          fL   of new length = f L of originallength .       f * (2/3) * 60  =   340 * 60 .        f =  510 Hz   isthe new freq . (b) The idea here is that the guitarist causes a node atthe fret location and the string oscillates in the n =3 mode. .         So the freq of theharmonic is    3 * 340 =   1020 Hz

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