Answer:
[tex]f=81.96 \ Hz[/tex]
Explanation:
Givens
[tex]L=95cm[/tex]
[tex]m_{sculpture} =13kg[/tex]
[tex]m_{wire}=5g[/tex]
The frequency is defined by
[tex]f=\frac{v}{\lambda}[/tex]
Where [tex]v[/tex] is the speed of the wave in the string and [tex]\lambda[/tex] is its wave length.
The wave length is defined as [tex]\lambda = 2L = 2(0.95m)=1.9m[/tex]
Now, to find the speed, we need the tension of the wire and its linear mass density
[tex]v=\sqrt{\frac{T}{\mu} }[/tex]
Where [tex]\mu=\frac{0.005kg}{0.95m}= 5.26 \times 10^{-3}[/tex] and the tension is defined as [tex]T=m_{sculpture} g=13kg(9.81 m/s^{2} )=127.53N[/tex]
Replacing this value, the speed is
[tex]v=\sqrt{\frac{127.53N}{5.26 \times 10^{-3} } }=155.71 m/s[/tex]
Then, we replace the speed and the wave length in the first equation
[tex]f=\frac{v}{\lambda}\\f=\frac{155.71 m/s}{1.9m}\\ f=81.96Hz[/tex]
Therefore, the frequency is [tex]f=81.96 \ Hz[/tex]
