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

Step-by-step 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{(T)/(\mu )}`

where
`v=wave\ speed`

`T=tension`

`\mu =linear\ mass\ density`

`\mu =(T)/(v^2)`

wavelength for this wave
`\lambda=2L=2* 0.864=1.728\ m`

and
`v=f* \lambda`

`v=24.03* 1.728`

`v=41.52\ m/s`

`\mu =(T)/(v^2)`

`\mu =(5.24)/(41.52^2)`

`\mu =3.04* 10^(-3)\ kg/m`