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Lorico [155]
3 years ago
7

A 13 kg hanging sculpture is suspended by a 95-cm-long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundame

ntal frequency. What is the frequency of the hum

Physics
2 answers:
Valentin [98]3 years ago
8 0

Explanation:

Below is an attachment containing the solution.

Artyom0805 [142]3 years ago
3 0

Answer:

f=81.96 \ Hz

Explanation:

Givens

L=95cm

m_{sculpture} =13kg

m_{wire}=5g

The frequency is defined by

f=\frac{v}{\lambda}

Where v is the speed of the wave in the string and \lambda is its wave length.

The wave length is defined as \lambda = 2L = 2(0.95m)=1.9m

Now, to find the speed, we need the tension of the wire and its linear mass density

v=\sqrt{\frac{T}{\mu} }

Where \mu=\frac{0.005kg}{0.95m}= 5.26 \times 10^{-3} and the tension is defined as T=m_{sculpture} g=13kg(9.81 m/s^{2} )=127.53N

Replacing this value, the speed is

v=\sqrt{\frac{127.53N}{5.26 \times 10^{-3} } }=155.71 m/s

Then, we replace the speed and the wave length in the first equation

f=\frac{v}{\lambda}\\f=\frac{155.71 m/s}{1.9m}\\ f=81.96Hz

Therefore, the frequency is f=81.96 \ Hz

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