308 E A R L E C. GREGG, JR. 



where p is the density of the medium and the other symbols are de- 

 fined as before. This relation allows the pressure to be calculated in 

 terms of the amplitude: 



P = 2wfpVA (6) 



For a source of area S (S large compared to X^), the mean power 

 radiated becomes: 



Power = y2pV{2TTfAYS (7) 



For example, consider a typical quartz disc vibrating at a frequencj'' 

 of 500 kilocycles per second and delivering a sound intensity of about 

 10 watts per square centimeter (10^ ergs/sec. /cm. ^) into water. For 

 water, V = 1.48 X 10^ cm. per second and p = 1, so that we have 

 from equation (5) : 



P = (2pF/)'/^ = 5.4 X 106 dynes/cm.2 



or about 5.4 atmospheres. 



In this example then, the pressure alternates from +5.4 atmos- 

 pheres to —5.4 atmospheres 500,000 times a second. To calculate 

 the amplitude of vibration of the water molecules, we find from equa- 

 tion (6) that: 



A = {P/2wfpV) = 1.16 X 10-^ cm. (8) 



From the laws of simple harmonic motion (see equation 3), we further 

 find that the maximum acceleration of the particles is: 



a = Att^PA = 1.14 X 108 cm./sec.2 



or an acceleration about 10^ greater than that due to gravity. These 

 large accelerations account for much of the coagulating action of 

 ultrasonics and other related effects. Considering the above values, 

 ultrasonic fields have been correctly described as ''all acceleration 

 and no motion." 



It is worth while to point out here that, since the density of the 

 medium appears in the intensity equation, very large amplitudes of 

 vibration are required to produce a given acoustic intensity in a gas 

 as compared to a liquid, or solid. This fact coupled with energy con- 

 version efficiencies means that far different generating devices must 

 be used in the various media. The magnetostrictive and piezoelec- 

 tric generators discussed later are adapted primarily to production of 



