Firstly, IANAQP, but here is my intuitive understanding.
When playing a bugle, high notes are all close together in pitch because with short wavelength, adding one makes a proportionally small change. Playing lower notes, the notes are further apart - there are effectively fewer notes in the lower ranges because adding one extra wavelength makes a big difference to the pitch.
Similarly the wavelengths of particles between the plates. When the plates are far apart, pretty much every wavelength can appear between them, so things are the same inside as out. When the plates are close together, fewer particles/waves can appear between because their wavelength must divide the distance, while the ones outside are still unrestricted. Then there are simply more of them, resulting in a higher pressure.
When playing a bugle, high notes are all close together in pitch because with short wavelength, adding one makes a proportionally small change. Playing lower notes, the notes are further apart - there are effectively fewer notes in the lower ranges because adding one extra wavelength makes a big difference to the pitch.
Similarly the wavelengths of particles between the plates. When the plates are far apart, pretty much every wavelength can appear between them, so things are the same inside as out. When the plates are close together, fewer particles/waves can appear between because their wavelength must divide the distance, while the ones outside are still unrestricted. Then there are simply more of them, resulting in a higher pressure.