6 SOUND WAVES 



D. Condensation. — A new term will now be introduced. Condensation 

 is defined as the ratio of the increment of density change to the original 

 density, 



s = 1.6 



p 



Combining equations 1.5 and 1.6 



£l = ('SV = (I + s)y := I + ys 1.7 



po \p/ 

 or po' = po + pays 1.8 



The excess pressure, or instantaneous sound pressure p, is po' — po. 



p = pQ-ys 1.9 



The instantaneous sound pressure at a point is the total instantaneous 

 pressure at that point minus the static pressure. The unit is the dyne per 

 square centimeter. This is often called excess pressure. 



The effective sound pressure at a point is the root-mean-square value of 

 the instantaneous sound pressure over a complete cycle, at that point. 

 The unit is the dyne per square centimeter. The term " effective 

 sound pressure " is frequently shortened to " sound pressure." 



The maximum sound pressure for any given cycle is the maximum 

 absolute value of the instantaneous sound pressure during that cycle. 

 The unit is the dyne per square centimeter. In the case of a sinusoidal 

 sound wave this maximum sound pressure is also called the pressure am- 

 plitude. 



The peak sound pressure for any specified time interval is the maxi- 

 mum absolute value of the instantaneous sound pressure in that interval. 

 The unit is the dyne per square centimeter. 



A dyne per square centimeter is the unit of sound pressure. 



E. jy Alembertian Wave Equation. — The three equations 1.2, 1.4 and 

 1.5 characterize disturbances of any amplitude. The first two are non- 

 linear save for small amplitudes. In general, acoustic waves are of in- 

 finitesimal amplitudes, the alternating pressure is small compared with 

 the atmospheric pressure and the wavelength is so long that «, o, w and s 

 change very little with x, y and 2. Substituting equation 1.6 in 1.2 and 

 neglecting high order terms, 



ds du dv dw ^ ^ ^^ 



-+ — + — +— = 1.10 



dt dx dy dz 



