3. Some guitarists like the feel of a set of strings that all have the same tension. For such a guitar, the G string (196 Hz) has a mass density of 0.31 g/m. What is the mass density of the A string (110 Hz)

0.98 g/m

Explanation:

Note: Since Tension and frequency are constant,

Applying,

F₁²M₁ = F₂²M₂ Equation 1

Where F₁ = Frequency of the G string, F₂ = Frequency of the A string, M₁ = mass density of the G string, M₂ = mass density of the A string.

make M₂ the subject of the equation

M₂ = F₁²M₁/F₂² Equation 2

From the question,

Given: F₁ = 196 Hz, M₁ = 0.31 g/m, F₂ = 110 Hz

Substitute these values into equation 2

M₂ = 196²(0.31)/110²

M₂ = 0.98 g/m

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