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Chapter 17: Q. 38 (page 484)

Tendons are, essentially, elastic cords stretched between two fixed ends. As such, they can support standing waves. A woman has a 20-cm-long Achilles tendon—connecting the heel to a muscle in the calf—with a cross-section area of 90 mm2.. The density of tendon tissue is 1100 kg/m3. For a reasonable tension of 500 N, what will be the fundamental frequency of her Achilles tendon?

Short Answer

Expert verified

The fundamental frequency of the tendon is 177.5 Hz

Step by step solution

01

Write the given information 

The length of the tendon, L= 20 cm = 0.2m
Area of cross section, A= 90 mm2 = 90x 10-6 m2
The density of the tendon, ρ= 1100 kg/ m3
The tension in the string, T= 500N

02

To determine the fundamental frequency of tendon 

The mass per unit length of the string is given by
µ=ρA=(1100kg/m3)(90x10-6m2)=0.099kg/m

The frequency of the tendon is given by

f=12LTµ=12(0.2)500N0.099kg/m=2.5(71)=177.5Hz

Thus, the fundamental frequency of the tendon is 177.5 Hz

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