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