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kudoushinichi88
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Homework Statement
An aluminium block of m is hung from a steel wire of length L. The fundamental
frequency for transverse standing waves on the wire is 300 Hz. The block
is then immersed in water so that half of its volume is submerged. What is the
new fundamental frequency? (You may assume that the mass of the wire is small
compared to the mass of the block and the change in length of the wire under
different loads is negligible.)
Homework Equations
Speed of wave on a string,
[tex]v=\sqrt{\frac{T}{\mu}}[/tex]
Buoyancy force
[tex]F=\rho g V[/tex]
The Attempt at a Solution
[tex]\frac{fL}{2}=\sqrt{\frac{T}{\mu}}[/tex]
when suspended in air,
[tex]150L=\sqrt{\frac{mg}{\mu}}[/tex]
When half of its volume immersed in water,
[tex]\frac{fL}{2}=\sqrt{\frac{mg-\frac{\rho_{water}gV}{2}}{\mu}}=\sqrt{\frac{mg-\frac{\rho_{water}mg}{2\rho_{Al}}}{\mu}}[/tex]
The answer I got is
[tex]f=300\sqrt{1-\frac{\rho_{water}}{2\rho_{Al}}[/tex]
Subbing in values gives me a value of 270Hz...
are my steps correct?
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