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Suppose a guitar is tuned to drop D tuning. This means that the notes from the...

Suppose a guitar is tuned to drop D tuning. This means that the notes from the 6th string to 1st string are D-A-D-G-B-E. Compute what the spring constants of each string must be once each has achieved its tension after being tuned. Must have a differential equation.

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Answer #1

Drop D tuning is an alternative form of guitar tuning in which the lowest (sixth) string is tuned down from the usual E of standard tuning by one whole step to D. Drop D tuning, as well as other lowered altered tunings, are often used with the electric guitar in heavy metal music.

The mechanical energy of an element of the string is :

dE(x,t)=12[T0(∂y∂x)2+μ(∂y∂t)2]dxdE(x,t)=12[T0(∂y∂x)2+μ(∂y∂t)2]dx

Where T0T0 is the tension at rest and μμ is the linear mass density.

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