Question

A heavy piece of hanging sculpture is suspended by a90-cm-long, 5.0 g steel wire. When the wind

blows hard, the wire hums at its fundamental frequency of 80Hz. What is the mass of the
sculpture?

Answer 1

As we know that fundamental frequency is given as

`f = (1)/(2L)\sqrt{(T)/(\mu)}`

here we know that

`\mu = (m)/(l)`

here we have

m = mass of wire = 5 g

l = length of wire = 90 cm

`\mu = (0.005)/(0.90) kg/m`

`\mu = 5.56 * 10^(-3) kg/m`

from above formula now

`80 = (1)/(2(0.90))\sqrt{(T)/(5.56* 10^(-3))}`

`144 = √(180 T)`

`T = 115.2 N`

now we know that tension is due to weight of the sculpture so we will have

`Mg = 115.2 N`

`M = 11.76 kg`

so its mass will be 11.76 kg