Question

(a) In a liquid with density $1300kg/m^3$, longitudinal waves with frequency 400Hz are found to have wavelength 4m. calculate the bulk modulus of the liquid.
(b) A metal bar with a length of 2m has density $6400kg/m^3$. 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. $33\times {10}^{9}N/m^2,1.6\times {10}^{11}N/m^2$
• B. $33\times {10}^{6}N/m^2,1.6\times {10}^{9}N/m^2$
• C. $66\times {10}^{9}N/m^2,3.2\times {10}^{11}N/m^2$
• D. $66\times {10}^{6}N/m^2,3.2\times {10}^{9}N/m^2$

Answer 1

The correct option is A $33\times {10}^{9}N/m^2,1.6\times {10}^{11}N/m^2$

(a) $v=f\lambda =\sqrt{\frac{B}{\rho }}$
$\therefore B=\rho (f\lambda {)}^2$
$=\left(1300\right)(400\times 4{)}^2=33\times {10}^{9}N/m^2$

(b) $v=\frac{l}{t}=\sqrt{\frac{Y}{\rho }}$
$\therefore Y=\rho {\left(\frac{l}{t}\right)}^2=\left(6400\right)\left(\frac{1.5}{3.9\times {10}^{-4}}\right)=1.6\times {10}^{11}N/m^2$