Acoustic impedance

 

Basic Principles

 

Acoustic impedance Z (or sound impedance) is the ratio of sound pressure p to particle velocity v. Also it is the product of the density of air ρ (rho) and the speed of sound c. The acoustic impedance Z is expressed in rayl (from Rayleigh, in  N·s·m-3=Pa·s/m):

Z = \frac{p}{v} = \frac{J}{v^2} = \frac{p^2}{J} = \rho \cdot c

with p = sound pressure, in N/m2 = Pa = pascal,
v = particle velocity in m/s,
J = sound intensity in W/m2,

ρ (rho) = density of the medium (air) air in kg/m3,

c = speed of sound (the acoustic wave velocity) in m/s.

 

v is the acoustic analogue of electric current, and p the analogue of voltage. Table 3 gives the densities (ρ), sound velocities (c) and acoustic impedance (Z) is of some bio-materials.

 

Table 1

 

In dry air at 20°C (68°F) the speed of sound is approximately 343 m/s, about 1 m each 3 ms. The velocity in brain, muscle and other bio-materials with a high water content, and trabecular bone is slightly higher. Fat has a slightly lower value of 1450 m/s and cortical bone with its much higher density (1.9·103 kg/m3) 4040 m/s.

Under normal conditions air is nearly a perfect gas, and so its speed does hardly depend on air pressure and on humidity.

 

Sound travels slower with an increased altitude, primarily as a result of temperature and humidity changes. The approximate speed (in m/s) is:

   (7)

where tC is the temperature in o C. A more accurate expression is

      (8)

where γ is the adiabatic index or cp/cV ratio, the ratio of heat capacity of the gas (cp) with constant p and the specific heat capacity of the gas (cV) with constant V, T the absolute temperature (K), and R (287.05 J/(kg·K) for air) the universal gas constant (see Gas laws) In this case, the gas constant R, which normally has units of J/(mol·K), is divided by the molar mass of air. The derivation can be found in various textbooks. For air γ = 1.402.

 

Application

 

Ultrasound  Sound speed is a basic parameter in ultrasound applications, especially for moving objects (like the valves of the heart) which movement is determined by the Doppler effect (see Doppler principle).

 

More info

 

Hearing   For an equal sound pressure in two materials, v is reciprocally with Z. For instance Zwater ≈ 4000 Zair, and so the particle velocity in water is 4000 smaller than that in air. Therefore, also the particle velocity of a sound impinging from a source in the air onto the head is 4000 times smaller than in the air. The resulting vibration of the head gives rise to bone conduction, but with respect to the sound sensation evoked by the pressure impinging onto the eardrum it is irrelevant.

Speed of sound   Under normal conditions air is nearly a perfect gas, and so its speed does hardly depend on air pressure and on humidity.

Sound travels slower with an increased altitude, primarily as a result of temperature and humidity changes. The approximate speed (in m/s) is:

   (7)

where tC is the temperature in o C. A more accurate expression is

      (8)

where γ is the adiabatic index or cp/cV ratio, the ratio of heat capacity of the gas (cp) with constant p and the specific heat capacity of the gas (cV) with constant V, T the absolute temperature (K), and R (287.05 J/(kg·K) for air) the universal gas constant (see Gas laws) In this case, the gas constant R, which normally has units of J/(mol·K), is divided by the molar mass of air. The derivation can be found in various textbooks. For air γ = 1.402.

 

See further  Sound and acoustics, Ultrasound and the Doppler principle.