I'm asking this to make a passive sound amplifiyer. In the web they usually do a HORN shape that looks like exponential function mirrored about 'x' axes. But I wonder is there a better shape for amplification. Perhaps maybe there are shapes for High frequencies and low ones. And assume the inlet sound as a phone speaker, round inlet or rectangular, both designs are ok.
The best shape for high frequencies (and some high mid) is the horn. But a horn can actually take many shapes. For example, its walls can be parallel like a didgeridoo. In fact, most, if not all, wind instruments are effectively differently tuned versions of the horn.
The reason the exponential horn is often used in loudspeakers (and this is an oversimplification) is an attempt to keep the frequency response as flat as possible for a certain range. If you look at wind instruments, the length and thickness (in fact the volume) of the parallel part of the tube is what tunes the instrument. You either alter the length by opening valves or by making the pipe loop longer like in a trumpet.
For bass frequencies you need a very big horn (see tuba), so in order to make it more compact, the horn is usually folded.
This is a very interesting (and creative) example of how a 'horn' can be folded and tuned.
I don't think my acoustics are good enough to go into more detail but this article on wind instruments should give almost all the information you need.
There is no such thing as "passive sound amplification". Sound energy does not fall from the sky.
Horn speakers merely do an impedance transform bringing the characteristics of the air at a solid sound source closer to that of the vibrating solid, transferring more of the sound energy: the air has a large resistance at a horn throat at the horn's operating frequencies. But that implies that the sound source needs to work differently than one designed for open space. Horn speaker drivers are built differently from normal speakers since a paper membrane is not great for transferring comparatively large forces at comparatively small movements.
And you want the inlet sound source to be a phone speaker, likely with a flimsy plastic dome membrane. The phone speaker is optimized for a certain application. Doing an impedance transform is not likely to make the materials happy.