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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?

Respuesta :

Answer:

Explanation:

Given

Length of tendon [tex]L=20\ cm[/tex]

Area of cross-section [tex]A=110\ mm^2[/tex]

Density of tendon [tex]\rho =1100\ kg/m^3[/tex]

Tension in the string [tex]T=500\ N[/tex]

Linear mass Density [tex]\mu =\frac{m}{L}[/tex]

[tex]\mu =\frac{\rho AL}{L}[/tex]

[tex]\mu =\rho \cdot A[/tex]

Fundamental Resonant frequency is given by

[tex]f=\frac{1}{2 L}\sqrt{\frac{T}{\rho A}}[/tex]

[tex]f=\frac{1}{2\times 0.2}\sqrt{\frac{500}{1100\times 110\times 10^{-6}}}[/tex]

[tex]f=160.70\ Hz[/tex]

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