Question

The velocity of the transverse waves in a wire of density $8000kg/m^3$ is $300m/s$. The tensile stress in the wire is then

• A. $7.2\times {10}^{8}N/m^2$
• B. $6.8\times {10}^{8}N/m^2$
• C. $5.2\times {10}^{8}N/m^2$
• D. $8.4\times {10}^{8}N/m^2$

Answer 1

The correct option is A $7.2\times {10}^{8}N/m^2$

Given density = 8000 $kg/m^3$ and velocity =300 m/s

Also we know velocity of transverse wave $\text{V}=\sqrt{\frac{T}{\mu }}\text{where T= tension and}\mu =\text{mass per unit lenght}=\frac{m}{L}$

also $\text{Density}\rho =\frac{mass}{Area\times Lenght}\rho \times A=\frac{m}{L}$

$\text{Tension T}=\rho A{V}^2$

We know stress $\sigma =\frac{Force}{Area}=\frac{Tension}{Area}=\frac{V^2\rho A}{A}=V^2\rho$

${300}^2\times 8000=7.2\times {10}^8\frac{N}{m^2}$