Impedance, acoustic fluids 32

Continuity of normal impedance follows immediately from continuity of traction and displacement. When one or both media is a solid, any incident wave will generate a longitudinal and one or two transverse waves in each solid, so that a fuller analysis is required (Auld 1973). A case of particular importance in acoustic microscopy is that of a wave in a fluid incident on... 

If the density pc of the cell is known, then the acoustic velocity in the cell can be immediately deduced, since vc = Zc/pc. Since determination of acoustic velocity by this method depends on the measurement of relative amplitudes, the amplifiers and their gain controls must be accurately calibrated. The combination of reflection and transmission coefficients on the right-hand side of (9.4) can be expressed in terms of the acoustic impedances of the coupling fluid, the cell, and the substrate. 

Z - ratio of acoustic impedance of cylinder fluid to acoustic impedance of water. 

The shear stresses developed by streaming velocities may affect the neighbouring tissue structures. Acoustic streaming may be important when the medium has an acoustic impedance different from that of its surroundings, the fluid in the biological medium is free to move or oontinuous waves are applied. 

ANL s ultrasonic viscometer is a nonintrusive in-line device that measures both fluid density and viscosity. The design of the viscometer is based on a technique that measures acoustic and shear impedance. The technique was first applied by Moore and McSkimin (1970) to measure dynamic shear properties of solvents and polystyrene solutions. The reflections of incident ultrasonic shear (1-10 MHz) and longitudinal waves (1 MHz), launched toward the surfaces of two transducer wedges that are in contact with the fluid, are measured. The reflection coefficients, along with the speed of sound in the fluid, are used to calculate fluid density and viscosity. Oblique incidence was commonly used because of better sensitivity, but mode-converted waves often occur in wedges that do not exhibit perfect crystal structure and lack well-polished surfaces. For practical applications, we use the normal-incidence arrangement. 

Acoustic impedance of a fluid Z/ is the product of fluid density p and phase velocity V of sound in the fluid it can be determined by measuring the reflection coefficient R at the boundary of the fluid and transducer wedge. If we select the normal-incidence configuration, R is given by... 

The bounding interface between the external and middle ear is the tympanic membrane. Pressure variations across the membrane move three ossicles, the malleus (hammer) connected to the membrane, the incus (anvil), and the stapes (stirrup) whose footplate is a piston-Hke structure fitting into the oval window, an opening to the fluid-filled cavities of the inner ear. Ligaments and muscles suspend the middle-ear ossicles so that they move freely. If sound reaches fluids of the inner ear directly, 99.9% of the energy is reflected [Wever and Lawrence, 1954], a 30-dB loss due to the mismatch in acoustic impedance between air and inner-ear fluids. Properties of the external meatus, middle-ear cavity, tympanic membrane, and middle-ear ossicles shape the responsiveness of a species to different frequencies. 

Note that / can be an arbitrary function of its scalar argument and the above would satisfy the equations of linear acoustics. For instance, for propagation along the jc-direction in a Cartesian coordinate system, rightgoing pressure waves of the formp =f x — c t) produce a velocity of the form vi = ipi/ipQCo), whereas left-going pressure waves of the form pi = g(x + cof) lead to the velocity vi = —ipi/(poco). Here, i is the unit vector in the increasing x direction. This becomes an important distinction when the problem of reflection and transmission of a wave across an interface between two media is considered. It is also seen that the product of fluid density and sound speed, poCo, provides the proportionality between pressure and speed. This combination occurs frequently in acoustics and is known as the acoustic impedance. 

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