Scale length is the length of the part of a guitar string that is free to vibrat

Question

Scale length is the length of the part of a guitar string that is free to vibrate. A standard value of scale length for an acoustic guitar is

25.5 in. The frequency of the fundamental standing wave on a string is determined by the string's scale length, tension, and linear mass density. The standard frequencies f to which the strings of a six-string guitar are tuned are given in (Figure 1) . Assume that a typical value of the tension of a guitar string is 84.0 N (although tension varies somewhat for different strings).

Part A

Calculate the linear mass density for the E2 string.

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Part B

Calculate the linear mass density for the G3 string.

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Part C

Calculate the linear mass density for the E4 string.

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Part D

Just before your band is going to perform, your G3 string breaks. The only replacement string you have is an E2. If your strings have the linear mass densities calculated in the previous parts, what must be the tension in the replacement string to bring its fundamental frequency to the G3 value of 196.0 Hz?

Express your answer with the appropriate units.

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Part A

Calculate the linear mass density for the E2 string.

E2 = g/cm

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Part B

Calculate the linear mass density for the G3 string.

G3 = g/cm

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Part C

Calculate the linear mass density for the E4 string.

E4 = g/cm

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Part D

Just before your band is going to perform, your G3 string breaks. The only replacement string you have is an E2. If your strings have the linear mass densities calculated in the previous parts, what must be the tension in the replacement string to bring its fundamental frequency to the G3 value of 196.0 Hz?

Express your answer with the appropriate units.

F =

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Explanation / Answer

= T / v^2

is density of string , T is tension on string and v is frequency of string

A.)

in E2 = 84/ 82.4^2 = 0.01237 kg/m = 0.123 g/cm

B.) in G3

in G3 = 84/ 196^2 = 2.18*10^-3 kg/m = 0.0218 g/cm

C.)   in E4 = 84/ 329.6^2 = 7.732*10^-4 kg/m^3 = 07.73 *10^-3 g/cm

D.) tension = v^2 * = 196^2 * 0.01237 = 475.20 N

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