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 130 mm^2. The density of tendon tissue is 1100 kg/m^3.

Required:
For a reasonable tension of 600 , what will be the fundamental resonant frequency of her Achilles tendon?

Answer 1

161.938 Hz

Step-by-step explanation:

the computation of the fundamental resonant frequency is shown below

p = 1100 kg/m^3

A = 130 mm^2

= 130 ×10^-6 m^2

T = 600 N

L = 20 cm

= 0.2 m

Now the linear density of tendon is

= 1100 kg/m^3 × 130 ×10^-6

= 0.143 kg/m

Now the wave of the string is

= √600 ÷ √0.143

= 64.775 m/s

Now finally the fundamental resonant frequency is

= 64.775 ÷ (2 × 0.2)

=161.938 Hz