Question

- The elastic limit of the steel forming a piece of wire is equal to 2.70 ×108 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress?( The density of steel is 7.86 × 103 Kg/m3

Answer 1

The elastic limit of the steel forming a piece of wire is equal to $2.70 \times 108 \, \text{Pa}$. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress? (The density of steel is $7.86 \times 103 \, \text{Kg/m}^3$)

Propagation speed in the wire:

$$c = \sqrt{\frac{T}{\delta}}$$

where $T$ – wire tension, $\delta$ – linear density.

$$c = \sqrt{\frac{T}{\frac{m}{l}}} = \sqrt{\frac{T}{\frac{\rho V}{l}}} = \sqrt{\frac{T}{\frac{\rho S l}{l}}} = \sqrt{\frac{T}{\rho S}} = \sqrt{\frac{P}{\rho}}$$ $$c_{max} = \sqrt{\frac{2.7 \times 10^{8} \, \text{Pa}}{7.86 \times 10^{3} \, \text{kg/m}^3}} = 185.34 \, \text{m/s}$$

Answer: $c_{max} = 185.34 \, \text{m/s}$