316 EARLE C. GREGG, JR. 



If we assume that the effect of clamping and a water load are negli- 

 gible, it follows then from the previous relationships that this ampli- 

 tude in water represents an intensity of 0.47 watt per square centi- 

 meter. By using higher magnetizing fields and operating the bar at 

 resonance (24 kilocycles), some investigators have achieved intensi- 

 ties as high as 20 Avatts per square centimeter. 



As is well known, the frequency of vibration of a rod depends upon 

 where it is clamped. Although there are many different modes of 

 vibration, the rod will vibrate strongly only when it is clamped at a 

 node, the position of the desired node along the rod being determined 

 by the harmonic selected. However, since the energy output di- 

 minishes considerably when a rod is clamped to produce higher har- 

 monics, it is the general practice to clamp rods in the middle in order 

 to produce intense vibration at the fundamental frequency. This 

 central clamp also provides a suitable mechanical support for the rod. 

 In practice, the position of this clamp may have to be adjusted for 

 maximum output since the two ends of a rod are often loaded un- 

 equally; as a result a node will not occur at the exact center. Al- 

 though magnetostrictive sources of ultrasound have been developed 

 that utilize rods or tubes clamped at one end, these have not been 

 generally used or found adaptable to biological research. Tubes 

 clamped in the middle have proved the simplest to construct and 

 operate. 



The natural frequency of any rod or tube is given by : 



/„. = (n/26)(^/p)'/' (12) 



where E is Young's modulus, p the density, h the length, and n the 

 harmonic for which it is clamped (1, p. 135). Since the frequency is 

 inversely proportional to the length, one limit to the frequencies 

 attainable is the physical size of the rod. For example, if a nickel 

 rod were to vibrate at a fundamental frequency of 50 kilocycles, its 

 length would be only 5.07 cm. Rods shorter than this become not 

 only less convenient to handle but also more difficult to excite. 

 Harmonics may be used, but, as mentioned, there is a resultant loss 

 of intensity. Pierce (5) has designed some special rods for high fre- 

 quencies. 



When any metal is introduced into an alternating magnetic field, 

 localized (eddy) currents are generated in the metal and thus part of 

 the electrical energy is converted to heat. Hence, the presence of 

 these parasitic currents lowers the efficiency of conversion of electrical 



