Chapter 12, Problem 9Q

To determine

Why the frets of a guitar are closed together at the top?

Answer to Problem 9Q

Solution:

Distance is proportional to frequency

Explanation of Solution

A wire fixed at both ends will resonate proportional to $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$L$}\right.$. To change the frequency by one octave the frequency is cut in half. The longer the string is, the larger the distance between the frets has same proportional changes in frequency.