Some Problems in Sound Radiation

This study concerns the determination of the total power output of acoustic sources in a fluid medium. Three geometries, with variations, are considered, and, in each case, the power radiated is calculated by analytical methods. The first geometry studied is a finite length cylindrical shell of harmonic monopoles. Variations in the phase and strength of the source distribution are made, and the effect of a uniform axial flow is also considered. The second geometry is a rigid parallel walled duct with a transverse slot cut in one wall. This slot can be covered with a membrane or flexible plate. A point source, located outside the duct, emits radiation which sets in motion the fluid in the slot region. The effect of the surface on the power radiated to the duct, and to the external fluid, is studied for small fluid loading. The third problem concerns a subsonic round jet with a slug velocity profile. The jet contains a monopole on its axis. The monopole is either stationary, or it is convected with the same velocity as the jet. For both the cylinder and the jet problems, the method employed for the determination of the power radiated requires an integration only over the source region itself. This technique can greatly simplify the task of power calculation, as compared to the more traditional method of flux integration in the far field. This is in particular true for the case of a distributed source in flow, here the cylinder, for which flux integration leads to an intractable problem. Traditional flux integration techniques are used for the duct problem in order to determine the partition of energy between the regions. This result is checked by the alternate method for power calculation used in the other problems.