Question

a) What is the Young’s modulus of a metal if the speed of the sound in a rod is 4550 m/s and it’s density is p=5230 kg/m3?

b) A sound wave propagates through a 10 cm closed tube. The air temperature is -8 Celsius degrees. Calculate the second and third harmonics.

Answer 1

a) $v=\sqrt{E/\rho}\to E=v^2\rho=4550^2\cdot5230=108.3\ (GPa)$

b) $f=\frac{nv}{2L}$ ; $v=\sqrt{\gamma\frac{RT}{M}}=\sqrt{1.4\cdot\frac{8.31\cdot265}{0.029}}=326\ (m/s)$

$f_2=\frac{2\cdot326}{2\cdot0.1}=3260\ (Hz)$

$f_3=\frac{3\cdot326}{2\cdot0.1}=4890\ (Hz)$