but only when the measuring frequency is high. The main 

 limitation is that the sound beam must be long enough to 

 cause a reasonable amount of attenuation. This places 

 a practical restriction on attenuation measurements 

 with this equipment to frequencies above 1 Mc/s. 1 



Plane waves can also be obtained by letting the wave 

 propagation take place inside a tube of a material with a 

 much higher specific acoustic impedance than the fluid 

 under investigation. This requirement can be met easily 

 for gases, since pc of steel is about 10 5 times larger than 

 pc of air (p being the density of material and c the sound 

 speed). The same ratio for steel and water, however, is 

 only about 2 5. 



Tube interferometers have nevertheless been success- 

 fully used on liquids and mixtures of liquids with water as 

 the main constituent, but only under special circumstances. lS ~ 19 

 These methods would not be suitable in the present problem, 

 since the attenuation in many cases is too small to allow 

 the utilization of a tube of reasonable length. Furthermore 

 a difficulty is encountered in the presence of air bubbles 

 on the wall. This is the same difficulty explained later 

 under resonating cavities. In the case of fluids which con- 

 tain a high density of bubbles within the fluid itself, the 

 presence of the bubbles may actually enhance the use of 

 the tube interferometer since the acoustic impedance of 

 the fluid is thereby lowered while the absorption coefficient 

 is increased. 19 



LABORATORY METHODS: THREE-DIMENSIONAL 

 WAVE PROPAGATION 



There are two subgroups in this division: reverberant 

 chambers and resonant chambers . The reverberation 

 methods all utilize a "diffuse" sound field, i.e., a very 

 large number of normal modes are energized at the same 

 time, and these modes must be close together in frequency. 

 The volume of the sample required is therefore quite large, 



