The question asks about both a violin and a loudspeaker. It would make sense to imagine that these were closely analogous, and I initially thought they would be, but after researching this a little more online, I think the physics is actually completely different.
Violin et al.
I think this analysis applies to any member of the violin family, including viola, cello, and double bass. It should also apply to a guitar and other stringed instruments that have a soundboard.
I wrote up a relatively nontechnical answer to this on music.SE, so anyone who wants a less densely technical discussion could take a look at that. The instrument has a resonance of air breathing in and out through the f-holes, and also a set of complicated resonances of the soundboard, the ones that we commonly see visualized as Chladni patterns. The important point about the soundboard resonances is that the ones that are actually excited by the instrument all seem (based on the sources I've seen) to be dipoles or higher-order multipoles. These don't radiate much power when the wavelength is long compared to the size of the soundboard, because there is strong cancellation between parts of the soundboard oscillating with opposite phases.
There are lots of possible speaker designs out there, but a common one for good audio quality is a sealed enclosure with a speaker cone sitting on a suspension and driven electromagnetically. The driver (cone+suspension, not sure if I'm getting the terminology right) has a spring constant $k_s$ and a quality factor $Q$, with typically $Q\approx 1$ for good-quality audio. In addition to the spring constant of the suspension $k_s$, we have a spring constant due to the spring of the air inside the enclosure, $k_a\propto 1/V$, where $V$ is the volume. These spring constants add, so no matter what, you can't have $k<k_a$. Therefore if you make the volume of the speaker too low, you get a big $k$ and a high resonant frequency. At low frequencies, the roll-off of the Lorentzian response of this resonator is 12 db/octave, and this ensures that if the volume is small, the response at low frequencies will be weak.
Of course this doesn't mean that no other type of design can ever evade this physical restriction. IIRC there are all kinds of interesting designs out there, including things like ribbons that work through electric rather than magnetic fields. However, my impression is that if you want realistic bass with good audio quality (good transient response and other criteria), usually the best engineering trade-off at most price ranges today is still something governed by the physics I've described above.
Even for this design, it's not totally obvious to me why you can't do things like increasing the mass of the driver to make the resonant frequency lower. Maybe that requires impractically large magnet coils?