Answer:
161.9 Hz ( fundamental resonant frequency )
other resonant frequencies: 323.85 Hz, 485.7 Hz..
Explanation:
Given:
A= 130 [tex]mm^{2}[/tex] => 130 x [tex]10^{-6}[/tex] [tex]m^{2}[/tex]
Tension T= 600N
Length L= 20cm= 0.2m
Density of tendon ρ= 1100 kg/[tex]m^{3}[/tex]
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 [tex]10^{-6}[/tex] => 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= [tex]\sqrt{\frac{600}{0.143} }[/tex]
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 ([tex]\frac{v}{2L}[/tex] ) where m= 1,2,3,4,.....
Therefore, fundamental resonant frequency of her Achilles tendon is:
[tex]f_{1}[/tex] = [tex]\frac{64.77}{2 * 0.2}[/tex] => 161.9 Hz
The other resonant frequencies can be find by integral multiples of frequence.
So,
[tex]f_{n} = n * f_{1}[/tex]
[tex]f_{2} = 2 * 161.9[/tex] = 323.85 Hz
[tex]f_{3} = 3 * 161.9[/tex] = 485.7 Hz
