Question

Derive a formula for linear mass density μ in terms of the wave speed v and string tension T, and enter it below. Assume you have the following experimental results: L = 0.864m f1 = 24.03Hz T = 5.24 N
What is the linear mass density of the string (without uncertainty, units requred)?

Answer 1

Answer:

Explanation:

Given

Length $L=0.864\ m$

frequency $f=24.03\ Hz$

Tension in the string $T=5.24\ N$

Wave speed in a string is given by

$v=\sqrt{\frac{T}{\mu }}$

where $v=wave\ speed$

$T=tension$

$\mu =linear\ mass\ density$

$\mu =\frac{T}{v^2}$

wavelength for this wave $\lambda=2L=2\times 0.864=1.728\ m$

and $v=f\times \lambda$

$v=24.03\times 1.728$

$v=41.52\ m/s$

$\mu =\frac{T}{v^2}$

$\mu =\frac{5.24}{41.52^2}$

$\mu =3.04\times 10^{-3}\ kg/m$