Appendix A 593 



The difference, cp 2 — <p l5 is called the phase difference. Under most con- 

 ditions, the ear is insensitive to phase differences, but for clicks, drum 

 beats, piano attacks, and so on, these phase differences between the 

 various audible components are very important. 



To those familiar with electrical theory, the analogies between 

 acoustics and electricity are striking. There are many analogies possible ; 

 one is presented in Table II. These analogs help the person trained in 



physics or engineering to apply to acoustics the mathematical symbolism 

 and proofs developed for electrical circuits and transmission lines. 



To use this analogy, it is customary to define a specific acoustic 

 impedance z, such that 



v 

 It is analogous to the electrical impedance Z, where 



Z = voltage/current 

 For plane waves going in the + x -direction 



2 = pc 



This value of z is called the characteristic impedance. 



When an electrical transmission line is joined to another element 

 having the same impedance, a maximum power transfer will occur. If 

 the two have an impedance ratio much different from one, relatively 

 little power transfer takes place. Likewise, if two acoustic media with 

 very different characteristic impedances are in contact, a plane wave 

 will be primarily reflected at the interface. For example, air has a 

 characteristic impedance 



P^air = 42 CgS UnitS 



whereas water and tissue have characteristic impedances 

 /^H 2 o — tissue — 1-5 x 1Q5 cgs units 



