Question

The middle C string on a piano is under a tension of 907 N. The period and wavelength of a wave on this string are 3.82 ms and 1.40 m, respectively. Find the linear density of the string.

Answer 1

The linear density of the spring = 0.00675 kg/m

Step-by-step explanation:

F₀ = 1/λ
`√(T/D)`........................ Equation 1

Making D the subject of formula in equation 1,

D = T/(F₀λ)²................................... Equation 2

Where F₀ = Frequency of the string, T = Tension, D = linear Density, λ = Wave length.

Given: T = 907 N, λ = 1.40 m

F₀ = 1/t, where t = period and t = 3.82 ms = 3.82 × 10⁻³ s

F₀ = 1/(3.82×10⁻³) = 10³/3.82 = 261.78 Hz.

Substituting these values into equation 2

D = 907/(1.4×261.78)²

D = 907/(366.492)²

D = 907/134316.39

D = 0.00675 kg/m

The linear density of the spring = 0.00675 kg/m