Question

ntroductory Physics I <Homework #3 Problem 16.53 Review Constants Periodic Table Part A 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 For a reasonable tension of 400 N what will be the fundamental resonant Express your answer with the appropriate units frequency of her Achilles tendon? 20-cm-long tendon with a cross-section area of 130 The density of tendon issue is 1100 kg/m Units Submit Pioide Feedack ype here to search

Answer 1

L = length = 20 cm = 0.20 m

A = area of cross-section = 130 mm² = 130 x 10^-6 m²

Volume is given as

V = A L

V = (130 x 10^-6) (0.20)

V = 26 x 10^-6 m³

$\rho$ = density = 1100 kg/m³

mass is given as

M = $\rho$V

inserting the values

M = (1100) (26 x 10^-6)

M = 0.0286 kg

m = mass per unit length = M/L = 0.0286/0.20 = 0.143 kg/m

T = tension force = 400 N

fundamental frequency is given as

f = (1/(2L)) sqrt(T/m)

f = (1/(2 x 0.20)) sqrt(400/0.143)

f = 132.2 Hz