46 



TESTING TECHNIQUE 



the effectiveness varies with frequency, at high fre- 

 quencies, where diffraction is less important, such an 

 arrangement of screens may reduce the effective re- 

 flection coefficient R by a factor of from l / 10 to i/ 2 . 

 The ease of construction and handling makes it prof- 

 itable to have such screens available for use. They 

 may also be used in an inverted "V" arrangement on 

 the bottom to reduce bottom reflections. 



ft would probably increase the effectiveness of a 

 screen to make it absorbing rather than perfectly 

 reflecting. However, until recently no suitable sound- 

 absorbing materials for underwater use have been 

 available, and it is not yet known how effective these 

 mav be. 



5.3.5 



Electric Signal Methods: 

 Thermal Noise, Warble 



There are several methods of reducing the effect 

 of reflection interference which have been used with 

 considerable success in air acoustics. These are based 

 on the fact that the cosine term in equation (3) is a 

 function of frequency, so that, if the response is 

 averaged over a band of frequencies, the oscillatory 

 effect of this term on the response, as the frequency is 

 varied, can be largely averaged out. Two methods of 

 doing this are by using a frequency which is warbled 

 about the frequency at which the response is desired, 

 and by using a band of thermal noise centered at the 

 frequency at which the response is deshed. The re- 

 sponse as measured by each of these methods is an 

 average over a band of frequencies of the response of 

 the instrument. The fact that a band of frequencies 

 rather than a single frequency is used limits the reso- 

 lution in response of the instrument. Rapid changes 

 in response become more gradual as measured by 

 this method. 



It may be shown that a signal which is warbled be- 

 tween frequencies /„ — A// 2 and f + A// 2, with a 

 warbling rate very much less than /,„ has frequencies 

 in its harmonic (Fourier) analysis covering essentially 

 the same frequency range as does the warbling. Simi- 

 larly, a band of noise of frequency breadth A/ cen- 

 tered at / also contains, by definition, frequencies in 

 this same band. It can be shown mathematically that, 

 to eliminate the effect of interference oscillations in 

 response by either of these methods, A/ must be deter- 

 mined by the inequality 



where A^ is the shortest difference in path between 

 the direct signal and any of the reflected signals. 72 



The extent to which one is interested in resolving 

 the frequency variations in response of an instrument 

 depends to a large extent on the type of instrument 

 being tested. The resolution attained in a method of 

 measurement of the response is defined in the follow- 

 ing manner: Consider an instrument which has two 

 very sharp response peaks at frequencies / — A// 2 

 and / + A//2. A method of measurement which is 

 just able to resolve the response into two maxima is 

 said to have a resolving power at the frequency / 

 equal to 



RP = -L. 



A/ 



(19) 



Therefore, the higher the resolving power, the greater 

 the definition with which the method can measure a 

 frequency response. For the average testing program, 

 it is usually satisfactory if the resolving power is equal 

 to 100 or 200 at all frequencies. For the use of warble 

 or noise, the resolving power is 



RP = J-< f 

 A/ 



c 



aI 



fAL 

 c 



(20) 



A/> 



AL 



(18) 



Hence, for any fixed frequency, the resolving power 

 is determined by AL. This limits seriously the use of 

 the method at low frequencies, since, with /\L fixed 

 as it is by the geometry of the test, the resolving power 

 decreases as the frequency is lowered. Thus for 

 AZ. = 5 feet, the maximum resolving power becomes 

 100 at 100 kc, 10 at 10 kc, 1 at 1 kc. For rough meas- 

 urements 10 might be admissible, but any lower 

 values for the resolving power would give very little 

 information of importance. Thus, it is only at high 

 frequencies that the method is of much value. 



These methods have another serious disadvantage. 

 After the oscillatory interference terms are elimi- 

 nated in the expression for the pressure, the pressure 

 that is measured is approximately the square root of 

 the sum of the squares of the pressures in the direct 

 wave and in all of the reflected waves reaching the re- 

 ceiver. Thus, the measured pressure is always greater 

 than the pressure in the direct wave alone. In some 

 cases, such as the measurement of directivity patterns, 

 the reflected waves are often higher in level than the 

 direct wave, so that in this case the direct wave is ac- 

 tually discriminated against by these methods. There- 



