- #1

- 129

- 2

## 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?

Last edited: