Question

A copper wire is held at the two ends by rigid supports. At 30 c the qire is just taut , with neglegible tension. ,/the speed of transverse waves in this wire at 1 c is

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, $v=\sqrt{\frac{F}{m}}$.......(1)

where m is linear mass density and F is force.

from thermal expansion,

∆l = $l\alpha\Delta\theta$

so, F=$Y\alpha A\Delta\theta$....(2)

and linear mass density = mass/length

= volume × density/length

= area × length × density /length

= area × density

= $A\rho$......(3)

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

$v=\sqrt{\frac{Y\alpha A\Delta\theta}{A\rho}}$

so, $v=\sqrt{\frac{Y\alpha\Delta\theta}{\rho}}$

here, Y = 1.3 × 10¹¹ N/m² , $\alpha$ = 1.7 × 10^-5 /°C , $\rho$ = 9 × 10³ Kg/m³ and $\Delta\theta=30-10=20$

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

= √{1.3 × 1.7 × 20 × 10³/9}

≈ 70 m/s

Answer 2

Answer:

70 m/s

Explanation: