Question

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

b) What is the fundamental frequency and second harmonic of a sound wave that propagates inside an open tube, if the air is at a temperature of 35 Celsius degrees? The length of the tube is 40 cm.

Answer 1

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

(b) $v=\sqrt{\gamma\frac{RT}{M}}=\sqrt{1.4\cdot\frac{8.31\cdot308}{0.029}}=352\ (m/s)$

$f=\frac{nv}{2L}\to f_1=\frac{352}{2\cdot0.4}=440\ (Hz)$

$f_2=\frac{2\cdot352}{2\cdot0.4}=880\ (Hz)$