Answer:
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
