Question

What is the fastest transverse wave that can be sent along a given wire? For safety reasons, the maximum tensile stress to which this wire should be subjected is 3.56 × 108 N/m2. The density of the wire is 8300 kg/m3. Note that your answer does not depend on the diameter of the wire.

Answer 1

The maximum tensile stress to which steel wires should be subjected is τ _max = 3.56 x 10^8N/m^2.

The density of steel ρ = 8300 kg/m^3.

Let the cross-sectional area of the wire =A

The Tensile strength of the wire= τ /A

The velocity of the transverse wave v_max =√(T / μ )

                                                             = √( τ L/ρV)

                                                             = √[(τ / A ) / ρ]

                                                             = √( τ _max / ρ)

= √( 3.56 x 10^8 / 8300 )

v_max = 207.103 m/s

From the above equation it is seen that the velocity is independent of the diameter of the wire.