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--long tendon with a cross-section area of 130 . The density of tendon tissue is 1100 .
For a reasonable tension of 600 , what will be the fundamental resonant frequency of her Achilles tendon?

161.9 Hz ( fundamental resonant frequency )

other resonant frequencies: 323.85 Hz, 485.7 Hz..

Explanation:

Given:

A= 130 => 130 x

Tension T= 600N

Length L= 20cm= 0.2m

Density of tendon ρ= 1100 kg/

Linear mass density is defines as:

μ = m/L =  ρV/ L =  ρAL / L

μ = ρA

where,

m=mass , V = volume,  L= length , A= cross section area and ρ= density

so, μ = 1100 x 130 x => 0.143 kg/m

Wave speed in the string is defines as

v=  sqrt(T/μ)

where,

T is string tension and μ is the linear mass density.

So,

v=  

v= 64.77 m/s

Frequencies of standing wave- modes of a string of length L fixed at both ends can be defines as:

fm = m ( )                where m= 1,2,3,4,.....

Therefore,  fundamental resonant frequency of her Achilles tendon is:

=   =>  161.9 Hz

The other resonant frequencies can be find by integral multiples of frequence.

So,

= 323.85 Hz

 = 485.7 Hz

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