ELIMINATION OF REFLECTIONS 



49 



5.3.7 



Corrections for Reflections 



In many tests it is found that the methods of elimi- 

 nating reflections so far described either are ineffec- 

 tive or, because of the particular nature of the test, 

 cannot be used. In such cases, one must correct the 

 results for the reflections which may have been pres- 

 ent during the test. The principal difficulty in mathe- 

 matically eliminating the effects of reflection inter- 

 ference is the decision as to whether variations in re- 

 sponse are a consequence of reflections or are inher- 

 ent characteristics of the instrument under test. Some 

 useful aids in identifying reflection interferences are 

 the following: 



f. If response measurements are made at different 

 testing distances, the difference in path length be- 

 tween the direct and reflected waves is not the same. 

 As a result, the interference maxima and minima in 

 the different response curves appear in different posi- 

 tions. Since variations in the inherent response char- 

 acteristic of the instrument under test are not shifted 

 by changing the testing distance, this forms a valuable 

 criterion for identifying reflection interferences. 



2. It was pointed out in Section 5.3.1 that reflec- 

 tion maxima or minima are spaced regularly with 

 frequency. This spacing between successive maxima 

 or minima is 



A/ = 



AL' 



(6) 



where c is the velocity of sound and A L is the differ- 

 ence in path between direct and reflected waves. 

 Thus, a periodicity of response maxima or minima 

 with frequency is often indicative of reflection inter- 

 ference and, with the geometry of the test known, one 

 can calculate the frequency spacing by equation (6) to 

 determine whether or not it coincides with the ob- 

 served values. If there is more than one prominent 

 reflection entering into the test, however, this criter- 

 ion becomes difficult to apply, since there are maxima 

 and minima introduced by interference between the 

 direct waves and each reflected wave and between the 

 various reflected waves themselves. The resultant ef- 

 fect on the response is qtiite confusing and makes it 

 difficult to determine unambiguously whether varia- 

 tions are due to reflection interference or are charac- 

 teristic of the instrument. 



3. In calibrating sound sources, two receivers with 

 different directivity patterns may be used. In such 

 cases, reflection interferences have different magni- 



tudes or positions in the two frequency-response 

 curves. This fact is often an aid in deciding whether 

 variations in response are due to reflections or are in- 

 herent in the instrument. 



Once the reflection maxima and minima have been 

 identified in a response curve, it is necessary to decide 

 how to eliminate them and obtain the inherent re- 

 sponse characteristic of the device under test. The 

 most useful method at higher frequencies makes use 

 of the fact that, if the reflection maxima and minima 

 are prominent and the direct and reflected signals do 

 not vary too rapidly with frequency, the maxima ap- 

 pear at frequencies where the direct and reflected 

 signals are in phase, and the minima where they are 

 out of phase. Hence, at a maximum, one measures the 

 sum of the signals in the direct and reflected waves, 

 and at a minimum, their difference. If one takes the 

 signal voltages at a maximum and at an adjacent 

 minimum, the arithmetic mean of these two values 

 gives approximately the correct value. 



Probably the best way to make use of this principle 

 is the following: Find the difference in level in db 

 between each maximum and its two adjacent minima. 

 Plot each difference against a function (£(/) of the 

 mean frequency between that at the maximum and 

 that at the minimum. The points may be connected 

 in a smooth curve. Let D(f) be the voltage generated 

 by the hydrophone due to the direct acoustic signal at 

 sound frequency / and R(f), the voltage from the re- 

 flected signal. The measured value at a maximum is 

 expressed by D(f) + R(f) and at a minimum by D(f) — 

 R(f). If these are expressed in db from the usual basic 

 level, the equation for the curve becomes 



</,(/) = 20 log [ D(f) + R(f) ] - 20 log [ D(f) - R(f) ] 



20 log r 



= 20 log 



D(f) - R(f) ' 

 £>(/) + R(f). 



R(f) 

 D(f) 



R(f) 



(29) 



From this equation, R(f)/D(f) can be determined. 



To evaluate D(f), which is the quantity desired, 

 make use of the identity 



201og£>(/) = 20 log [£>(/) + #(/)] 



- 20 log [l +g!|]. ( 3 °) 



