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Guitar strings' lengths and relative densities, find their frequencies and tensions.

Given two guitar strings' lengths and relative densities, find information about their frequencies and tensions.

The thinnest string on a certain guitar has a linear density one fifteenth the linear density of the thickest string. Both strings are the same length, L= .64 m.

NOTE: On a musical scale a note one octave higher than a certain note is twice the frequency of that note.

PART a. If both strings have the same tension force, find the ratio of their two fundamental frequencies, 'fhi / flo'.

PART b. The fundamental note (first harmonic) of the thicker string is135 cy/sec, and its linear density is .006 kg/m. Find the tension in this string.

PART c. Find the frequency and the tension in the thinner string if it is to produce a note which is 3 octaves above the fundamental note of the thicker string.

Solution Preview

Preliminary: You need to recall that in general, the frequency f emitted by a string of a musical instrument is:
(1) f= (n/ 2L) (sqrt[F/ d]) in which:
n is the number of the harmonic (the fundamental note is the first harmonic so n=1) ,
L is the length of the string,
F is the tension in ...

Solution Summary

The solution presents a step by step process to arrive at the answers. The guitar strings' lengths, relative densities, frequencies and tension are found.