A standard guitar, whether acoustic or electric, has six strings, all with essen
ID: 1718962 • Letter: A
Question
A standard guitar, whether acoustic or electric, has six strings, all with essentially the same total length between the bridge and the nut at the tuning head. Each string vibrates at a different frequency determined by the tension on the string and the mass per unit length of the string. In order to create pitches (notes) other than these six, the guitarist presses te strings down against the fretboard, thus shortening the length of the string and changing their frequencies. In other words, the vibrating frequency of a string depends on tension length, and mass per unit length of the string.
The equation for the fundamental frequency of a vibrating string is given by
where
f = frequency [Hz] T = string tension [N]
Many electric guitars have a device often called a "whammy" bar or a "tremolo" bar that allows the guitarist to change the tension on the strings quickly and easily, thus changing the frequency of the strings. (Think of Jimi Hendrix simulating "the rockets red glare, the bombs bursting in air" in his rendition of The Star Spangled Banner - a true tour de force.) In designing a new whammy bar, we test our design by collecting data on a single string of the observed frequency at different lengths (using the fret board) with a specific setting of the whammy bar.
Length (L)[m] 0.25 0.28 0.32 0.36 0.40 0.45 0.51 0.57 0.64 Frequency (f)[Hz] 292 241 231 205 171 165 136 129 112Explanation / Answer
sqrt(T/mu) = 2 * L * f
sqrt(T1/mu) = 2 * 0.25 * 292 = 146
sqrt(T2/mu) = 2 * 0.28 * 241 = 134.96
sqrt(T3/mu) = 2 * 0.32 * 231 = 147.84
sqrt(T4/mu) = 2 * 0.36 * 205 = 147.6
sqrt(T5/mu) = 2 * 0.4 * 171 = 136.8
sqrt(T6/mu) = 2 * 0.45 * 165 = 148.5
sqrt(T7/mu) = 2 * 0.57 * 129 = 147.06
sqrt(T8/mu) = 2 * 0.64 * 112 = 143.36
Nothing else is specified in the question
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