TRANSMITTING 



21 



power. Thus, formulating the mathematical expres- 

 sion for the response, 



R T = 20 log — £= = 20 log p - 10 log P , . (3) 

 ' V Pa 



In equation (3), 20 log p gives the pressure in deci- 

 bels versus 1 dyne per sq cm (1 dyne per sq cm is called 

 reference pressure) and 10 log P A is the power level 

 referred to 1 watt. For actual testing, the practice of 

 expressing power levels in decibeJs versus 10 _lli watt 

 has developed. 



It will be noted that 1 meter is chosen for the refer- 

 ence distance. This, of course, does not mean that all 

 calibrations are to be made at that distance. The ac- 

 tual testing distance will depend on considerations oi 

 obtaining waves which are sufficiently plane so that 

 spherical wave corrections will not be required either 

 for the projector under test or for the receiving hydro- 

 phone, that is, the testing distance will depend on 

 the size of the instruments and the frequency. Other- 

 wise, the testing distance will be made as short as pos- 

 sible to minimize interference from reflections, etc. 

 The testing distance d will be stated in connection 

 with all tests and the correction C in decibels to d„ = 

 1 meter will be made on the basis of spherical waves; 

 thus 



C = 20 log 



d 



(4) 



A similar consideration applies with respect to the 

 power to be used in the tests. While the response is 

 referred to 1 watt, it would obviously be incorrect to 

 make all tests at that power level. If the device is 

 linear, the testing power used is of no consequence, 

 but if the response varies with power level, then the 

 tests should be made at the actual working levels used 

 in service and the testing power should be stated. A 

 load characteristic should be furnished showing the 

 relation between acoustic power output (or pressure 

 on the axis) and available power. 



4.1.3 



Directivity 



The next item to be measured concerns the distri- 

 bution of the acoustic pressure with direction. This 

 is measured by determining the pressure over a spher- 

 ical surface having the projector as the center, the 

 pressure p in any one direction being expressed in 



Figure 3. Three-dimensional directivity pattern for a 

 circular plate. Frequency = 25 kc. diameter of plate = 15 

 in. Decibel values shown give response relative to that on 

 hoi nial axis. 



decibels versus the pressure p„ on the acoustic axis of 

 the device. For the acoustic axis an axis of symmetry 

 ol the device is usually chosen, which frequently is 

 also the direction of maximum response. A plot of 

 these values is called a directivity pattern. A view of 

 a three-dimensional directivity pattern for a circular 

 plate is shown in Figure 3. For devices which are sym- 

 metrical, such as a circular plate, the directivity is the 

 same in all planes containing the major axis normal 

 to the surface. Thus the pressure distribution need be 

 measured only in one plane, resulting in a great re- 

 duction of work. A planar directivity pattern is 

 shown in Figure 4. This is the usual way of plotting 

 these patterns. Devices which are not circular usually 

 have several major axes. Patterns should then be 

 taken in all planes containing one of these axes. 



The directivity index is defined as the ratio in deci- 

 bels of the intensity / (/ = — far awav from the source) 



averaged over all directions to the intensity /„ on the 

 acoustic axis of the device: 



A 



lOlog- 



20 log 





(5) 



