Question

A metal bar with a length of 1.50 m has density 6400 $\frac{kg}{m^3}$.Longitudinal sound waves take $3.90\times {10}^{-4}$ s to travel from one end of the bar to the other. What is Young's modulus for this metal?

• A. $9.47\times {10}^{10}\frac{N}{m^{-2}}$
• B. $2\times {10}^{10}\frac{N}{m^{-2}}$
• C. $10\times {10}^{10}\frac{N}{m^{-2}}$
• D. None of these

Answer 1

The correct option is A

$9.47\times {10}^{10}\frac{N}{m^{-2}}$

Speed of sound in the metal bar$\frac{lengthofbar}{time}$

Speed $v=\frac{1.5}{3.9\times {10}^{-4}}=3846.1m{s}^{-1}$

Also speed of sound in a solid bar $v=\sqrt{\frac{Y}{\rho }}$

$\rho =6400\frac{kg}{m^3}$

$3846.1=\sqrt{\frac{Y}{6400}}$

$Y=9.47\times {10}^{10}N{m}^{-2}$