Question

A heavy anvil is suspended by a 0.75 m long steel wire that has a mass of 12 g. When the wire is plucked, it hums at its fundamental frequency of 120 Hz. What is the mass of the anvil?

Answer 1

Step-by-step explanation:

It is given that,

length of steel wire, l = 0.75 m

Mass of the wire, m = 12 g = 0.012 kg

Fundamental frequency, f = 120 Hz

We need to find the mass of the anvil (m'). The fundamental frequency is given by :

`f=(v)/(2l)`

v is the speed of the mass

Speed is given by :

`v=\sqrt{(T)/(\mu)}`

`\mu` is the mass per unit length,
`\mu=(m)/(l)`

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

T is the tension in the wire,

`f=(1)/(2l)\sqrt{(Tl)/(m)}`

`T=4f^2lm`

`T=4(120)^2* 0.75* 0.012`

T = 518.4 N

Tension in the wire, T = m' g

`m'=(T)/(g)`

`m'=(518.4)/(9.8)`

m' = 52.89 kg

So, the mass of the anvil is 52.89 kg. Hence, this is the required solution.