X. ULTRASONIC VIBRATIONS 323 



dian plane but this is largely wasted effort unless the crystal radiates 

 to the same extent in both directions. This is rarely the case and 

 when the two faces see different loads, the median plane is no longer 

 a nodal plane. 



Consider a crystal (or tube) radiating sound into a medium of 

 infinite extent. Under these circumstances, the medium offers some 

 resistance to the motion of the crystal (it must if power is to be de- 

 livered to the mediimi) and effectively lowers its amplitude as shown 

 before. Now introduce a reflecting boundary in front of the radiat- 

 ing surface. The waves reflected to the face of the crystal then act 

 either to damp the motion or to augment it depending on the phase 

 of the reflected wave relative to the motion of the vibrating surface. 

 As is readily seen, the relative phase of the two is determined by the 

 distance between the generating and reflecting surfaces. If the dis- 

 tance is adjusted so that the two are in phase (an integral number of 

 half wavelengths) a standing wave pattern results and the power de- 

 livered by the source is a maximum. This acoustic loading of the 

 crystal is reflected back to the electrical circuit and actually causes 

 the driving currents or voltages to change as the loading is changed. 

 Use is made of this phenomenon in acoustic interferometrj^ {2, p. 

 57). 



While the sound fields used in most biological work are too com- 

 plex to be analyzed in terms of simple plane wave reflections between 

 two surfaces, it remains that the introduction of specimens into the 

 sound field not only changes considerably the character of the sound 

 field but also changes the amplitude of vibration of the source. This 

 should be remembered when measurements of the sound field are 

 attempted. 



To obtain a variable frequency source of sound it is possible to 

 excite a quartz crystal to any amplitude at any frequency however 

 far from resonance as long as the exciting voltage does not exceed the 

 dielectric breakdown strength of the crystal. As far as mechanical 

 shatter is concerned, it may be said that the danger of shatter Avith 

 forced vibrations at high voltage is no greater than resonant vibra- 

 tions at low voltage. However, the forcing of a crystal off resonance 

 is very uneconomical as is seen from the resonance curves. Even if 

 it were economical to use high voltage at off-resonant frequencies, 

 the crystal would most likely be shattered, even with liquid damping, 

 if by chance the frequency happened to pass through resonance. 

 Resonant frequencies and a series of crystals are usually employed 



