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BELL SYSTEM TECHNICAL JOURNAL 



integers to Hxs and fiz's. Fig. 6.23 shows a plot of these three types of inter- 

 fering modes on a folded frequency scale covering the range from 5 to 15 

 megacycles for a plate 1 centimeter square. Each abscissae covers a range of 

 one megacycle with dots at three levels. The first level shows the fre- 

 quencies at which successive even orders of flexure along the X axis occurs. 

 The second level shows successive odd Zj shear modes along X and the third 

 level successive odd Z^ shear modes along Z' . The circles shown on the three 

 levels indicate the results of actual measurements on i^T-cut crystals as 

 resonating elements. It will be noticed that the circles and dots coincide 

 for most frequencies, the regions of departure occur only when a high order 

 shear mode and a high order flexure mode along the -Y axis approach each 



Fig. 6.23 — Frequencies at which the Z',. shear along A', the Z'x shear along Z' and the Xy 

 flexure along A' coincide with the high frequency A'j, shear in ST-cut crystals. 



other in frequency. The reason for this is obvious from the previous dis- 

 cussion on the coupling between flexure and shear modes of motion. 



The chart of Fig. 6.23 is of course not limited to a crystal 1 centimeter 

 square or for that matter even a square crystal. In reality it relates the 

 product of the frequency and X and Z' dimensions. For example a flexure 

 mode interferes with the high frequency shear mode at a frequency of 9.45 

 megacycles for a plate with X dimension equal to 1 centimeter. If the X 

 and Y' dimensions were doubled the same situation would exist at one half 

 the frequency. In determining the dimensions for a crystal at a given fre- 

 quency we know that the product of the frequency and X dimensions as well 

 as Z' dimension must not result in a frequency close to those given by the 

 circles of Fig. 6.23. In addition other interfering modes as previously 

 mentioned must be avoided. These at present may be determined experi- 

 mentally by choosing regions on the chart clear of the known flexure and 

 shear modes. 



