Question

The acoustic impedance of air:Zair=410kg/m2s. A sound wave propagates in air. 0.2% of the sound transmitted into an unknown material. the density of the unknown material is 3×10 to the power 3 kg/me. calculate the speed of sound in the unknown material in the unit of m/s.

Answer 1

The ratio of the intensity of sound transmitted to the incident intensity is given by:

where Z is the acoustic impedance of the unknown material.

Here, it is given that I_transmitted/I_incident = 0.2% = 0.002

so,

=>

=> 0.002 Z² - 1638.36 Z + 336.2 = 0

solving this quadratic equation gives two positive value of Z to be, Z = 0.2052 kg/m²s and Z = 819179 kg/m²s

The smaller value can be neglected since sound is traveling from a rarer (air) to denser medium and so a small transmission implies large reflection and thus a large acoustic impedance. Therefore, Z = 819179 kg/m²s

Acoustic impedance is related to density and speed of sound in that medium by:

Z = Dv

=> 819179 = 3 x 10³ v

=> v = 273 m/s.

This is the speed of sound in the given material.