X. ULTRASONIC VIBRATIONS 307 



manner as light reflections in optics. Likewise the portion of the 

 sound energy transmitted through the object may also be treated in a 

 manner similar to light incident on lenses and prisms since the object 

 undoubtedly has a different sound velocity than the medium in 

 which it is immersed (and hence an "acoustic" refractive index). 

 Such sound lenses and i)risms have been constructed and constitute a 

 very important tool in ultrasonics. Photograph D in Figure 1 con- 

 stitutes an experimental verification of this made by Willard (23). 



If the wavelength of the sound is large compared to the object 

 (about twice object size or larger), the object both refracts and reflects 

 the beam and creates a new type sound field in its vicinity. The 

 magnitude of the effect is determined by the ratio of wavelength to 

 object size. The larger this ratio, the less the effect until finally the 

 object becomes "invisible" to the sound. For intermediate ratios, 

 the problem is very difficult to calculate. 



For plane waves, it is easy to visualize a condition in which the 

 sound is reflected from a plane boundary back to the source and then 

 back to the boundary again. If the various direct and reflected 

 waves present at one point all vary in the same manner at the same 

 time (that is, if the reflector is an integral number of half wavelengths 

 away from the source), a "stationary" wave is said to be present. A 

 stationary wave is characterized by the fact that, as one moves 

 through the sound path, the amplitude of vibration passes through 

 well defined maxima and minima. These are known as loops and 

 nodes when dealing with dust patterns, organ pipes, and vibrating 

 strings in the audible sound range. 



Even when dealing with plane ultrasonic waves, the container (or 

 boundaries) has a very important bearing on the type of sound field 

 present owing to these multiple reflections. The results of any given 

 investigation that did not take this into account might be diflficult 

 to interpret correctly. (For a more complete discussion, refer to 

 Section CI.) 



4. Intensity 



Sound intensity is defined as the energy that passes through a 

 unit area in unit time. The dimensions are usually ergs per second 

 per square centimeter, or watts per square centimeter. For a plane 

 sound wave, the intensity, /, may be shown to be {1, p. 55) : 



/ = (pF/2)(27rM)2 = (PV2py) (5) 



