478 



SEISMIC METHODS 



[Chap. 9 



The acoustic resistance of a medium determines the load or energy output 

 of a sound source within, hence, also, the name radiation resistance or 

 impedance. It also controls the transmission of energy from one medium 

 to another and the ratio of reflected to incident energy. If the specific 

 acoustic resistances of two adjacent media differ considerably, almost no 

 energy is transmitted and nearly perfect reflection occurs. In the case of 

 energy transfer from water to air and vice versa, the amount transmitted 

 is only about 0.12 per cent of the incident energy. The same holds true 

 for the transmission of sound from an orifice or tubing of small diameter 

 to another of larger diameter. The case is analogous to the transmission 

 of sound from a rare to a dense medium. 



In the reverse case, when sound is trans- 

 mitted from a dense to a rare medium, or 

 from an orifice of large diameter into one of 

 smaller diameter, the transmitted energy is 

 still small as before (most of the incident en- 

 ergy being reflected), and the transmitted 

 amplitude is approximately twice that of the 

 incident amplitude. If a wave passes from 

 a medium with the specific acoustic resist- 

 ance Ri to another with the specific acoustic 

 resistance R2 , if Ai is the amplitude of the 

 direct wave, Bi the amplitude of the reflected 

 wave in the first medium, and A2 the ampli- 

 tude of the energy transmitted into the 

 second medium (see Fig. 9-22) then 



Fig. 9-22. Refracted and re- 

 flected rays in two media of 

 different specific acoustic re- 

 sistances. 



■D A ^2 ~ Ri . ri-2 ~ 1 , 

 ^' - ^^rT+Ri - ^^r-^I^ + l' 



2Ri ^ 2 



R2 -\- Ri ri_2 4* 1 



(9-34) 



A2 = Ai 



where ri_2 = R2/R1 .^^ The power transmission ratio is given by the 

 expression 4/(ri_2 +1)^; that is, the energy transmission from one medium 

 into another is poor if the specific acoustic resistances of two adjoining 

 media, such as air and water, differ widely. This may be remedied by 

 placing a third medium of intermediate specific acoustic resistance between 



1^ See G. W. Stewart and R. B. Lindsay, Acoustics, Van Nostrand (1930). 



^* Note the similarity of the coefficient 



(fii — Pi) 



Rj — Ri 



R2 +Ri 



with the reflection coefficient 



and the "dimming factor" 2pi/0>2 + pi) in the equations involving electrical 



(P2 -|- Pi) 



potentials in media of different resistivities p (see p. 712). 



