Tension in a wire due to a standing wave

[moonkey]

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.

 

[anathema]

Yes, your calculation appears to be correct. The tension on the wire would indeed be quite large due to the high density of steel and the small diameter of the wire. It's always a good idea to double check your calculations and units to make sure they are consistent.