Question

A copper rod of square cross section is fixed between two rigid support

Answer 1

your question is incomplete. A complete question is -------> A copper wire is held at the two ends by rigid supports. At 30° C, the wire is just taut, with negligible tension. Find the speed of transverse waves in this wire at 10° C.

Given: Young modulus of copper = 1.3 x 10¹¹ N/m2. Coefficient of linear expansion of copper = 1.7 x 10-5 ° C-1. Density of copper = 9 x 10³ kg/m3.

solution : we know, formula of speed of transverse wave, .......(1)

where m is linear mass density and F is force.

from thermal expansion,

∆l =

so, F=....(2)

and linear mass density = mass/length

= volume × density/length

= area × length × density /length

= area × density

= ......(3)

putting equation (2) and (3) in equation (1),

so,

here, Y = 1.3 × 10¹¹ N/m² ,  = 1.7 × 10^-5 /°C ,  = 9 × 10³ Kg/m³ and

so, v = √{1.3 × 10¹¹ × 1.7 × 10^-5 × 20/9 × 10³}

= √{1.3 × 1.7 × 20 × 10³/9}