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Physics- sound

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As the drawing shows, the length of a guitar string is 0.628 m. The frets are numbered for convenience. A performer can play a musical scale on a single string, because the spacing between the frets is designed according to the following rule: When the string is pushed against any fret j, the fundamental frequency of the shortened string is larger by a factor of the twelfth root of two (122) than it is when the string is pushed against the fret j - 1. Assuming that the tension in the string is the same for any note, find the spacing between fret 6 and fret 5.
Our professor discussed the velocity of guitar strings, but nothing about spacing. Is the space between the frets a wavelength? Any ideas on what equation to use?

No. The spacing between a fret and the end of string is a half wavelength.

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