Question

Calculate the stress in a tight wire of a material whose young’s modulus is $19.6\times {10}^{11}dyne/c{m}^2$, so that the speed of the longitudinal wave is 20 times the speed of transverse wave.

• A. $4.9\times {10}^{9}dyne/c{m}^2$
• B. $9.8\times {10}^{9}dyne/c{m}^2$
• C. $4.9\times {10}^{11}dyne/c{m}^2$
• D. $9.8\times {10}^{11}dyne/c{m}^2$

Answer 1

The correct option is A $4.9\times {10}^{9}dyne/c{m}^2$

Speed of longitudinal wave, $v_l=\sqrt{\frac{Y}{\rho }}$
Speed of transverse wave, $v_t=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{T}{\rho A}}$
Given, $v_l=20v_t\Rightarrow \sqrt{\frac{Y}{\rho }}=20\sqrt{\frac{T}{\rho A}}\Rightarrow \frac{T}{A}=\frac{Y}{400}=4.9\times {10}^{9}dyne/c{m}^2$