> as lemmas

1919 A. G. Webster in Proc. National Acad. Sci. U.S.A. 5 275 (heading) Acoustical impedance, and the theory of horns and of the phonograph.

1919 A. G. Webster in Proc. National Acad. Sci. U.S.A. 5 275 The term ‘impedance’..has been productive of very great convenience in the theory of alternating currents of electricity. Unfortunately, engineers have not seemed to notice that the idea may be made as useful in mechanics and acoustics as in electricity. In fact, in such apparatus as the telephone one may combine the notions of electrical and mechanical impedance with great advantage.

1919 A. G. Webster in Proc. National Acad. Sci. U.S.A. 5 275 If we have any oscillating system into which a volume of air X periodically enters under an excess pressure p, I propose to define the impedance by the complex ratio Z = p/X.

1927 I. B. Crandall Theory Vibrating Syst. ii. 71 In most parts of the text it is convenient to take the mechanical impedance as the ratio of maximum force to maximum velocity. Strictly, the velocity is analogous to current density rather than to total current... The acoustic impedance per unit area, divided by the area, is what corresponds most closely to the electrical impedance.

1934 N. W. McLachlan Loud Speakers i. 4 The difference between acoustical and mechanical impedance must not be confused. In the one case waves travel in some form of conduit or channel which impedes their progress. The greater the area the smaller the impedance. In the mechanical form something is being driven, so the greater the area driving the medium the greater the impedance opposing motion.

1936 P. M. Morse Vibration & Sound vi. 192 A consideration of the behavior of the specific acoustic impedance of a plane wave will enable us to work out the details of its interaction with various mechanical systems.

1953 Sci. News 29 11 Whenever in the layers lying below the bed of the sea there is a sudden change in the acoustic impedance (that is in the product of the density of the material and the velocity of sound waves in it), there is a reflecting boundary.

1955 T. F. Hueter & R. H. Bolt Sonics ii. 33 The concept of acoustic impedance is useful in the analysis of lumped systems, such as cavity resonators, sirens, jets, etc.

1960 R. B. Lindsay Mech. Radiation ix. 218 The excess pressure in a sound wave is taken to correspond with the electromotive force, and the volume current (the product of the particle velocity ξ and the area of the wavefront S) is assumed to be analogous to the electric current. Hence it is natural to define the acoustic impedance of a wave as Z = Pe/Ẋ, where Ẋ = volume current = Sξ. With the use of the complex notation for wave quantities the impedance will usually be complex. We first examine..the case of a plane harmonic wave of angular frequency w... The impedance of such a wave is then Z = ρ₀V/S, a real quantity. The numerator is called the specific acoustic impedance of a plane wave and denoted by Z_s. It is the impedance for a unit area of wavefront.

1961 W. G. Bickley & A. Talbot Introd. Theory Vibrating Syst. xi. 139 The example is that of torsional waves on a shaft... The [angular] velocity is proportional to the transmitted torque... Now in the electrical analogy the ratio of force to velocity is that of e.m.f. to current, a ratio which the electrical engineer calls impedance. It is therefore convenient to call the ratio of transmitted torque to angular velocity (and the analogous quantity in other cases) the transmission impedance.

1963 C. T. Morrow Shock & Vibration Engin. I. vi. 127 A high impedance indicates that even a large force results in little motion; it suggests massiveness and rigidity. A low impedance indicates that motion is easy to produce; it suggests lightness and flexibility. A resistive impedance indicates that the energy supplied at the point is absorbed, as in a dashpot... A reactive impedance indicates that energy supplied is stored, as in..a compressed spring.