BASIC DEFINITIONS 



237 



sure of 1 dyne per sq cm. In the past, sound levels 

 were frequently reported in decibels above 0.0002 

 dyne per sq cm. 



10.1.3 



Source Level 



The source level is a measure of the power output 

 of a sound source on the decibel scale. Briefly, it is 

 the sound level due to a point source at a distance of 

 1 yd, in decibels above 1 dyne per sq cm. If a point 

 source is located in a homogeneous, nondissipative 

 medium which is infinitely extended in all directions, 

 the intensity of the sound field is inversely propor- 

 tional to the square of the distance from the source, 





(3) 



This law is called the inverse square law. In terms of 

 the sound level, equation (3) becomes 



L = S - 20 log r. (4) 



In these equations, F and S are constants which de- 

 pend on the power output of the source, and r de- 

 notes the distance (slant range) from the source. 

 That S is the source level as defined above can be 

 verified by setting r equal to 1 in equation (4). 



For real sound sources in real media, equations (31 

 and (4) are not everywhere valid. Because of the 

 finite extension of an actual sound source, the in- 

 verse square law fails at ranges of the order of the 

 dimensions of the source. Because of absorption of 

 the sound in the medium and because of scattering 

 and reflection from bounding surfaces, it fails at very 

 long ranges. However, there is frequently an inter- 

 mediate range interval for which equation (4) holds. 

 If there is such an interval, then the constant S 

 is considered the source level, even though <S maj-^ 

 not be the actual sound level at a distance of 1 yd. 



For a highly directional sound source, such as a 

 standard echo-ranging transducer, the definition of 

 the source level is further specified by the condition 

 that the sound measurements are to be carried out 

 on the axis, that is, the radial line of greatest sound 

 field intensity. 



10.1.4 Transmission Loss and 

 Transmission Anomaly 



The transmission loss H at the range r is defined 

 by the formula 



H{r) = S- L{r), (5) 



where S is the source level, and L is the sound level 

 defined by equation (2). The transmission loss de- 

 fined in this way measures the drop of the sound 

 level with increasing distance from the source and 

 has the virtue of being independent of the particular 

 power output of the source. Other parameters of the 

 source, such as operating frequency and directivity 

 pattern, are known to affect the value of the func- 

 tion H{r). The units of H are decibels. 



The transmission anomaly A is the deviation of the 

 transmission loss from that functional behavior de- 

 manded by the inverse square law of spreading. The 

 defining equation for A{r) is 



A{r) = H(r) -20logr = S - L{r) - 20 log r. (6) 



The transmission anomaly vanishes if the inverse 

 square law of spreading is satisfied, and it is positive 

 if the sound level drops off more rapidly than 20 log r. 

 Large positive transmission anomalies, therefore, 

 correspond to poor sound conditions. 



In sound transmission work, it has been customary 

 to train the projector in a horizontal plane on the re- 

 ceiving hydrophone, but not to tilt the acoustic axis 

 away from the horizontal. Hence, measured trans- 

 mission anomalies will be large for a close deep 

 hydrophone beneath the sound beam. 



In supersonic transmission work, it has been found 

 that when successive signals are transmitted a few 

 seconds apart over the same transmission path, the 

 received sound intensity is subject to irregular fluctu- 

 ations. Reported transmission anomafies always rep- 

 resent values which have been obtained by averaging 

 over a number of signals received during a brief 

 period so that much of this fluctuation is smoothed 

 out. 



10.1.5 Variance of Amplitudes 



The standard deviation of the individual pressure 

 amplitudes in a sample of signals, divided by the 

 average pressure amplitude for the sample, is called 

 the variance of amplitudes for the sample. This 

 variance is used as a measure of the fluctuation of re- 

 ceived sound intensity. Observed values of the vari- 

 ance are surmnarized in Sections 10.4.1 and 10.4.2. 



10.1.6 Deep and Shallow Water 



Water is effectively deep when bottom-reflected 

 sound is much weaker than the direct sound; other- 

 wise, the water is effectively shallow. Over the con- 

 tinental shelf (depth less than 100 fathoms) the 



