Question

A steel Wire hangs vertically from a fixed point supporting a weight of 80N at lower end.The diameter of the wire is 0.50mm and its length from the frequency fron the fixed point to the steel wire is 1.5m.if density of steel wire is 7.8×10^³kg/m³ then what is the fundamental frequency emitted from wire.
a)76Hz
b)176Hz
c) 50Hz
d)150Hz​

Answer 1

Given info : A steel Wire hangs vertically from a fixed point supporting a weight of 80N at lower end.The diameter of the wire is 0.50mm and its length from the frequency fron the fixed point to the steel wire is 1.5 m.

To find : the fundamental frequency emitted from wire is ...

solution : first find linear mass density of wire.

mass of wire , m  = volume of wire × density of wire = Vρ = Alρ

now linear mass density, μ = m/l = Aρ = πd²ρ/4

                                             = 3.14 × (0.5 × 10⁻³)² × 7.8 × 10³/4

                                             = 1.53 × 10⁻³ kg/m

now fundamental frequency emitted from wire, f = $\frac{1}{2l}\sqrt{\frac{T}{\mu} }$

     =   $\frac{1}{2\times1.5}\sqrt{\frac{80}{1.53\times10^{-3}} }$  = 76 Hz

therefore the fundamental frequency emitted from wire is 76 Hz.