LONGITUDINAL VIBRATION OF BARS 45 



are known, or the frequency of sound when the velocity, density and 

 Young's Modulus are known. 



Rods in which the longitudinal waves are excited by striking the ends 

 are used as standards of high frequency sounds, 5000 and above, where a 

 tuning fork is not very satisfactory. 



Longitudinal waves in a rod may be set up by electromagnetic, electro- 

 static or magnetostriction means. In the first case, if the rod is of mag- 

 netic material and is held near an electromagnet in which an alternating 

 current is flowing a longitudinal force will be set up in the rod. If the 

 frequency of the driving current is continuously variable, the rod will be 

 set into violent vibrations at the fundamental resonant frequency. If the 



SECOND OVERTONE THIRD HARMONIC 



Fig. 3.5. Modes of longitudinal vibrations of a free rod. The nodes and loops are indicated 



by N and L. 



plane end of a rod is placed near a metallic disk, the two plane surfaces 

 may be used to serve as plates of a condenser. An alternating current 

 sent through the condenser will cause an alternating force to be exerted 

 upon the end of the rod. The rod will be sent into violent vibrations 

 when the frequency of the impressed alternating current corresponds to 

 the fundamental frequency or one of the overtones. Magnetization of 

 magnetic materials produces small changes in the dimensions of these 

 materials. A rod of magnetic material placed in a coil of wire will expe- 

 rience a change in length corresponding to the alterations in the actuating 

 current. If the coil is part of the circuit of a vacuum tube oscillator, the 

 rod will vibrate and the vacuum tube will oscillate at the fundamental 

 frequency of the rod. Such a system is termed a magnetostriction sonic 

 or super sonic generator ^^ and may be used to produce sound waves in air 

 or any other medium. 



Pierce, G. W., Proc. Am. Acad. Arts and Set., Vol. 63, p. 1, 1928. 



