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