would presumably vary as the 8th power of Mach number, and I think a few rough 

 calculations suggest that the level would be so small that one couldn't expect to be able 

 to detect it. I should like to ask if he has done any experiments in which there was 

 a lifting surface somewhere in the flow. There is a connection between the fluctuations 

 in the lift on a solid body, and the amount of surface noise generated. The intensity 

 of the surface noise varies as the 6th power of the Mach number, and might therefore 

 be greater than that of the volume noise at low Mach numbers. 



I suppose the most favorable circumstances for generation of surface noise 

 might be some kind of flat plate edge-on to a stream. 



H. M. Fitzpatrick 



I know of no such experiments involving a jet and lifting surface except, of 

 course, the "jet-edge" studies mentioned. 



M. Strasberg 



When you try to do such an experiment you run into a complication. If you 

 put a plate in a jet — you are, I presume, thinking of a rigid plate which would not 

 oscillate in the jet, so that the radiation would be the kind which is associated with 

 the lift forces on the plate. What happens in practice when you try to do that is that 

 the plate itself cannot be made infinitely rigid, and begins to oscillate and respond to 

 local pressures the jet exerts. As a result of the oscillation of the plate, sound will be 

 radiated, which very much complicates any analysis of the experimental results. 



That sound which is radiated by a vibrating plate, excited into vibration by the 

 fluctuations of pressure on it, is a very important type of sound. A theoretical analysis 

 has been given by Dr. Kraichnan, who is, I see, a couple of rows behind you there. 



M. J. Lighthill 



I could make comments on this point. But I would like to say first how much, 

 how very much I enjoyed Dr. Fitzpatrick's lecture. He tried to say some things I would 

 disagree with, but he wasn't able to. I find myself in complete agreement with every- 

 thing he said. I think it was extremely desirable that a survey of that kind should 

 have been made. 



On the question raised by Dr. Batchelor, whether hydrodynamic sound of a 

 one-phase character (involving no bubbles of any kind) could be detectable, I suppose 

 that the dipole radiation due to moving a circular cylinder about in a fluid is one of 

 the most promising kinds. A lot of information about the sound radiated in this case 

 is available. Phillips (J. Fluid Mech. 1 (1956), p. 607) has recently correlated exten- 

 sive measurements by Holle and Gerrard in the range of Reynolds numbers from 400 

 to 40000, by means of a formula which gives 



pUHd 



P = 0.006 



a 3 



where P is the total acoustic power radiated, p the density, U the velocity of the 

 cylinder, / and d its length and diameter, and a the velocity of sound; and he gives 

 reasons why the constant should be independent of Reynolds number in the range in 

 which the wake is irregular but the boundary layer is laminar at separation. 



In water, if U — 30 knots, / = 10 ft. and d = ¥2 in., then the Reynolds number 

 is in this range (it is about 10 5 ), and the formula gives P — 10 -3 watt. 



C. A. Gongwer 



I concur, of course, the aeolian tone will be generated, but it only occurs in 



the fairly narrow range of Reynolds number associated with the Karman vortex street. 



I noticed Dr. Fitzpatrick's curve of the sound from the underwater jets, which 



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