Tension in a wire due to a standing wave

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moonkey
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Homework Statement


Question 8
A 2m long steel wire is mounted in an insulated bath of water containing 2000 litres of water.
(a) If the bath is a rectangle 2 m long and 1 m wide, what is the depth of the water
The wire vibrates with a fundamental frequency of the G above middle C (392 Hz). The velocity of
the wave on the wire is given by:
v = sqrt(T/μ);
where T is the tension, and μ is the mass per unit length of the wire.

(Ignore the whole thing about the water, it's to be used in subsequent parts of the question that I haven't posted)
(b) If the diameter of the steel wire is 2 mm, what is tension on the wire?



Homework Equations


Density of Steel: ρ = 7.8 x 103 kg/m3.


The Attempt at a Solution



v=sqrt(T/μ)=λf

λ=2L μ=ρV/L=ρπr2L/L=ρπr2

sqrt(T/ρπr2)=2Lf

T=4ρπr2L2f2

ρ=7.8x103 kg/m3, r=0.001m, L=2m, f=392Hz

T=(4)(7.8x103)(π)(0.001)2(2)2(392)2

T=60247.16N

Does this seem right? 60kN seems like a very large force.
 

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