Question

Tendons are, essentially, elastic cords stretched between two fixed ends; as such, they can support standing waves. These resonances can be undesirable. The Achilles tendon connects the heel with a muscle in the calf. A woman has a 20-cm-long tendon with a cross-section area of 110 mm². The density of tendon tissue is 1100 kg/m³. For a reasonable tension of 500 N, what will be the resonant frequencies of her Achilles tendon?

Answer 1

Step-by-step explanation:

Given

Length of tendon
`L=20\ cm`

Area of cross-section
`A=110\ mm^2`

Density of tendon
`\rho =1100\ kg/m^3`

Tension in the string
`T=500\ N`

Linear mass Density
`\mu =(m)/(L)`

`\mu =(\rho AL)/(L)`

`\mu =\rho \cdot A`

Fundamental Resonant frequency is given by

`f=(1)/(2 L)\sqrt{(T)/(\rho A)}`

`f=(1)/(2* 0.2)\sqrt{(500)/(1100* 110* 10^(-6))}`

`f=160.70\ Hz`