226 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



FREQUENCY IN C. 



asoo 



h • 100 FEET 



5000 



iapo, 



SO 



•I.ZS 



1.00 



■0.75 ^|'< 



•0.25 



.50 



fh 



e 



/ = Frequency. c = Velocity of sound in water. 



h = Depth of water. X = Horizontal wavelength of disturbance. 



Variation of wavelength and phase velocity with frequency for normal modes in shallow water. Velocity of 

 Density of bottom assumed 2 times density of water. 



Figure 27. 



sound in bottom assumed to be 1.5 X c. 



and pi > p, equation (24) cannot be satisfied if ii is 

 imaginary; this justifies the statement made in the 

 second sentence following equation (19). 



Graphs of the solutions of equation (24) are given 

 in Figure 27 for a typical set of values of C\, pi, and h. 

 Typical curves of the variation of pressure along a 

 vertical line are given in Figure 28, corresponding to 

 particular points on the graphs of Figure 27. As was 

 explained in Section 2.7. 1, it is customary, by analogy 

 with the terminology used in the theory of vibrating 

 systems of particles, to use the term "normal mode" 



to describe a state of vibration of the water and 

 bottom in which the pressure distribution is given by 

 equation (12); for modes of the present type this is 

 equivalent to a disturbance of the type shown in 

 Figure 28 and having an amplitude represented by a 

 horizontally moving sine wave. It is convenient to 

 identify families of these normal modes by the num- 

 ber of horizontal planes in the water, including the 

 free surface on which the pressure is always zero. 

 This number is called the order of the normal mode, 

 and is indicated by the labels "FIRST MODE," 



