The tension (t) in a string fixed across a 2 m length (l) is 100 n, and the fundamental frequency is measured to be 100 hz. what is the linear mass density of the string?

0.625 g/m

Explanation:

The fundamental frequency of a tensioned string is:

f = √(T/ρ) / (2L)

where T is the tension,

ρ is the mass per length linear density,

and L is the length of the string.

Solving for ρ:

2Lf = √(T/ρ)

4(Lf)² = T/ρ

ρ = T / (4(Lf)²)

Given T = 100 N, L = 2 m, and f = 100 Hz:

ρ = 100 / (4 (2×100)²)

ρ = 100 / (4 × 40000)

ρ = 1/1600

ρ = 0.000625 kg/m

ρ = 0.625 g/m

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