ESTABLISHMENT OF SOUND FIELDS 



61 



water. They are, therefore, of negligible practical 

 significance in underwater sound calibrations. 



As evidence of this, consider the use of a Rayleigh 

 disk. This is a thin circular disk suspended from a 

 fine torsion filament so that the plane of the disk 

 makes a definite angle 6 with the direction of propa- 

 gation of the sound wave. If the wave length is much 

 greater than the diameter of the disk, there is a torque 

 exerted on the disk of magnitude 



M = | prtV- sin 2 



(52) 



where p is the density of the medium, a the radius of 

 the disk, and v the rms particle velocity. Expressed 

 in terms of the pressure, this becomes 



9 a 3 



3 pc- 



(53) 



c being the velocity of sound. Thus, for the same pres- 

 sure in air and water, the ratio of the torque in water 

 to that in air will be 



M„ 



Pa c a 



Pw c i, 



5 = 6.7x 10- 



(54) 



Since torques obtained with the Rayleigh disk are 

 very dilficult to measure in air for any reasonable 

 sound pressures, one sees that it would be almost im- 

 possible to measure them in water, even if the experi- 

 mental difficulties in setting up the apparatus could 

 be overcome. The Rayleigh disk and similar methods 

 must be discarded, therefore, as impractical for abso- 

 lute calibration in water. 



Radiation pressure is essentially the steady pres- 

 sure exerted on a surface when sound is reflected 

 from the surface and is, like the torque in the Ray- 

 leigh disk, a second order effect. If a plane sound 

 wave strikes normally a completely reflecting surface, 

 the area of which is numerically much greater than 

 the wave length, the radiation pressure on the surface 

 is given by 



p = s(* + 1)4. 



I pc- 



(55) 



where k is the ratio of specific heats for the medium 

 (practically unity for liquids), p is the rms sound 

 pressure, p the density of the medium, and c the veloc- 

 ity of sound. For a sound pressure of 1 dyne per sq cm 

 in water, the radiation pressure would be about 1Q- 10 



dyne per sq cm. Obviously, for such low-pressure 

 measurements, very delicate apparatus is required, 

 so that the method is usually of little practical value 

 although it can be used in the laboratory with high 

 sound pressures such as may be developed by quartz 

 crystals at high frequencies. 



There are various other methods of calibration 

 characterized by the fact that an electroacoustic trans- 

 ducer is not used, but all are more or less subject to 

 the objection that the measurements are exceedingly 

 delicate. Some are based on the variation of the index 

 of refraction of a fluid with pressure or similar ef- 

 fects. They usually have a limited frequency range 

 over which they can be employed. In comparison 

 with the methods of calibration which can be per- 

 formed with relative ease, none of them has much 

 practical importance at the present time. Further in- 

 formation regarding them may be obtained by con- 

 sulting various reference works on acoustics and the 

 general acoustical literature. 



5.5.6 



The Reciprocity Method of 

 Calibration 



By far the most accurate, simple, and generally 

 useful method of absolute calibration is the so-called 

 reciprocity method, based on the reciprocity princi- 

 ple as applied to electroacoustic transducers. Once 

 its advantages are enumerated, the reasons for its 

 adoption as a standard method of obtaining absolute 

 calibrations by USRL are clear. These advantages 

 are: 



1. The method is apparently applicable over the 

 entire practical range of frequencies. 



2. The actual measurements are easily made and 

 are essentially similar to those employed in relative 

 calibrations (comparison method). 



3. The method can be used by relatively unskilled 

 personnel. 



4. The measurements may be carried out in the 

 field rapidly and easily. 



5. Though the accuracy of the method is at present 

 limited by reflection-interference difficulties, these 

 also limit the accuracy of comparison methods. 



6. If certain easily attainable conditions are main- 

 tained, there are no theoretical corrections to be ap- 

 plied to the results. 



7. Several independent calibrations can be per- 

 formed at the same time, giving an immediate check 

 on the accuracy of the results. 



