As you already understood, the simplest case of radiation is the case when we have plane wave. For example, when we have a flat surface of discontinuity, and if this is a oscillator like this, obviously the wave generate, generated by this oscillation would be the plane wave. The next simplest case is the case when we have breathing sphere. In other words, if you have a sphere like this. And if this sphere breathes omni-directionally, in other words, it oscillates independent with any angle, then the sound generated by this kind of breathing sphere would be spherical. Omni-directionally same phase can be preserved. The other next simplest case would be like this. Suppose we have two breathing spheres. But each breathing sphere radiates or oscillates out of phase. In other words, when this expand, this contract. Expand, contract. Expand, contract. Then, what we can immediately see is that there is a some surface, there is no sound propagation. For exa, for example in this case, in this surface there would be no sound propagation. And, and in this axis, there will be a very strong sound radiation compared with other angle. So we can see that the sound radiated by these two breathing sphere has some direction of propagation. That we call trembling sphere, because when I have this sphere and then if this sphere oscillate like this. Then the sound in this direction would be maximum. And the sound in this direction obviously there's no sound radiation in this direction. Therefore there is a directivity, so we will study about how sound is radiating. First by using breathing sphere case, and then by trembling sphere case. And using these two fundamentals, and the, and the physically tangible example, we will attempt to understand general sound radiation.