X. ULTRASONIC VIBRATIONS 305 



pared to the piston, the piston acts Uke a point source and radiates 

 a spherical sound wave. That is, the sound radiates in all directions 

 with the same amplitude at any given distance from the source. 



As the wavelength is diminished (source frequency increased), the 

 sound energy tends to become concentrated more and more in a given 

 direction (or "beamed") and for wavelengths very small compared to 

 the piston, it apj^roaches a plane wave. That is, nearly all the soimd 

 energy is then propagated in a unidirectional beam with cross section 

 of about the same dimensions as the piston. The general sound 

 pressure pattern of a source is spoken of as the "directivity" of the 

 source. The photographs in Figure 1 of this phenomenon were made 

 by Willard {23) utilizing the optical diffraction effects of a 10 mega- 

 cycle ultrasonic beam. They show: 



(A) Reflection of a narrow beam from glass plate G, then from upper 

 water-air surface of the medium. 



(B) Double reflection from the inside corner of a steel block (St) and 

 subsequent absorption of the beam n a wool pad (P). 



(C) Reflection of an ultrasonic beam from a cylindrical brass surface 

 (Br) giving the familiar caustic curve. 



(D) A beam focused at / by means of a planoconcave Lucite lens. 



(E) An ultrasonic beam produced by the concave quartz crystal, which 

 results in focusing. 



(F) Transmission of a broad beam through a tapered aluminum plate 

 (black in figure). Plate transmits for thicknesses that are multiples of 

 X/2. 



(G) Diffraction of beam around a wire 21 X in diameter; note that sound 

 reappears in the center of the shadow. 



It is readily seen that, if thermal and viscous losses are not pres- 

 ent, the pressure or amplitude of a spherical wave diminishes in- 

 versely as the distance from the source while there should be no varia- 

 tions at all wdth distance for a plane wave in a homogeneous medium. 



From the wavelengths calculated previously for ultrasonic fre- 

 quencies and considering the usual physical size of a sound source, it 

 is obvious that most ultrasonic waves are plane waves and may be 

 treated as such. 



The problem of what happens to a sound wave when it strikes a 

 boundary or object is also decided by the ratio of the wavelength to 

 the dimensions of the object (2, p. 299). If the wavelength is small 

 compared to the dimensions of the object (about 3^f o the object size 

 or smaller), a reflection takes place that may be treated in the same 



