6 



INTRODUCTION 



that the sound pulse had to travel "around the cor- 

 ner" to reach the microphone. In that case, sound 

 energy is obviously deflected around the obstruction; 

 and it can be shown that this energy does not travel 

 everyivhere in a direction normal to the sound front. 

 A rigorous treatment of these more involved cases 

 shows, nevertheless, that a direction of propagation 

 always can be defined in a natural and unique man- 

 ner. 



Intensity of the Sound Field 



Sound is weakened as it travels and at very great 

 distances from the sound source cannot be detected. 

 We specify the strength of the sound by its intensity. 

 Somid intensity is defined as the rate at which soimd 

 energy passes through an area 1 centimeter square 

 placed squarely in the path of the traveling sound. 



In theoretical studies soimd intensity is usually 

 expressed in imits of ergs per squarecentimeter. In en- 

 gineering work, on the other hand, it is usually more 

 practical to express intensities on a logarithmic scale 

 both because of the very wide range of sound inten- 

 sities in practice and because sound intensities are 

 frequently the product of several factors. Use of the 

 logarithmic scale narrows down the numerical range 

 between very faint and very loud sounds and also 

 simpUfies the computation of many sound intensities 

 by replacing multiplication by addition. 



The logarithmic scale in general use is the decibel 

 scale. This scale may be explained as follows. Sup- 

 pose we want to compare two sound intensities /i and 

 h. To find the decibel difference between /i and h, 

 the common logarithm (base 10) of the ratio Ii/h is 

 multipUed by 10. As an example, suppose the inten- 

 sity /i is 1,000,000 times the intensity I2. The loga- 

 rithm of 1,000,000, multiplied by 10, is 60. Thus the 

 intensity /i is 60 db above the intensity h- In many 

 studies it is the decibel difference between two dif- 

 ferent sounds rather than the absolute strength of 

 any one sound, which is of most interest and can be 

 most readily determined. 



The decibel scale is also suitable for expressing ab- 

 solute sound intensities. For this purpose, a standard 

 intensity is first selected, called the reference intensity 

 or reference level, and then all other sound field in- 

 tensities are expressed in terms of decibels above (or 

 below) the standard. Unfortunately, different stand- 

 ards have been used by different groups in under- 

 water soimd research. Sometimes, 10~" watt per sq 

 cm has been used as the standard since this is the usu- 

 ally accepted standard in air. More frequently, the 



reference level has been expressed in terms of the 

 sound pressure. 



Since sound represents vibrations and since vibra- 

 tions of a fluid (such as air or sea water) are associated 

 with periodic changes in the local pressure, the devia- 

 tion of instantaneous pressm-e from the hydrostatic 

 or atmospheric pressure may be used as a measure of 

 sound intensity. This excess pressure oscillates dur- 

 ing each cycle; therefore, the intensity must be ex- 

 pressed in terms of some averaged quantity. Since the 

 excess pressure is positive during one half of the cycle 

 and negative during the other, its arithmetic mean 

 vanishes. It is possible to obtain a nonvanishing 

 average quantity by considering the rms excess pres- 

 sure. In the case of a sinusoidal vibration, the rms 

 excess pressure is equal to l/-\/2j or 0.7 times the 

 maximum value of the excess pressure. It will be 

 shown in Chapter 2 that in a given medium the sound 

 intensity is proportional to the mean square excess 

 pressure. Two standards based on pressure have been 

 used in underwater sound studies. One is a sound in- 

 tensity corresponding to an rms excess pressure of 

 0.0002 dyne per sq cm. This standard has been re- 

 cently replaced by that of an intensity corresponding 

 to an rms excess pressure of 1 dyne per sq cm. When 

 sound field intensities are expressed on a decibel scale 

 relative to some standard intensity, they are usually 

 referred to as sound levels. 



1.3 PROPAGATION OF SOUND IN 

 THE SEA 



When the propagation of sound in the sea first be- 

 came a matter of prime mihtary importance, it was 

 hoped and expected that sound would travel along 

 straight fines from the source and that the sound 

 field intensity would decrease in accordance with the 

 simple inverse square law. However, this hope was 

 not reafized. Because of the pecuUar characteristics 

 of the ocean as a sound-transmitting medium, marked 

 deviations occur from both straight-line propagation 

 and inverse square intensity decay. 



Straight-line propagation of sound is to be expected 

 only if the velocity of propagation is constant 

 throughout the medium. In the ocean this condition 

 is usually violated primarily because of the variation 

 of temperature with depth. There is almost always 

 a layer in which the water temperature drops ap- 

 preciably with increasing depth. This layer may begin 

 right at the sea surface, or it may lie beneath a top 

 layer of constant temperature. In such a region of 



