As the drawing shows, the length of a guitar string is 0.734 m. Thefrets are num

Question

As the drawing shows, the length of a guitar string is 0.734 m. Thefrets are numbered for convenience. A performer can play a musicalscale on a single string because the spacing between thefrets is designed according to the following rule: Whenthe string is pushed against any fret j, thefundamental frequency of the shortened string is larger by a factorof the twelfth root of two than it is when the string is pushedagainst the fret j - 1. Assuming that thetension in the string is the same for any note, find thespacing (a) between fret 1 and fret 0and (b)between fret 7 and fret 6.

Explanation / Answer

frequency and wavelength are connected through  v=f. Natural frequency corresponds to the first normalmode(wavelength=twice the string's length). The higher pitch is (the higher frequency is) the shorterstring should be. multiplying frequency by factor a will shortenthe string by factor a= twelfth root of two Hence the difference between 0 and 1st fret is l/a,l denotes original length Difference beten 6th and 7th frets will be(1/a6-1/a7)l

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