Tendons are, essentially, elastic cords stretched between two fixed ends; as suc

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 110mm2. The density of tendon tissue is 1100 kg/m3.

For a reasonable tension of 500N , what will be the fundamental resonant frequency of her Achilles tendon?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Fundamental resonant frequency (f) of a cord under tension is given by:

f = (1/2L)?(T/?)

where L is the length of the cord, T is the tension and ? is the linear density of the cord.

{We need to be consistent with our units. Everything in metres!}

Linear density ? = density * cross sectional area {kg/m = kg/m^3 * m

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