to be dumb, the sobbing of infants
喑 centers on voicelessness: being unable to speak or making only muffled, choked sounds. The sobbing of infants is a specific application of that same idea of suppressed or inarticulate vocalization.
喑 combines 口 (mouth) with 音 (sound), suggesting a mouth that cannot produce clear sound. The exact historical development is uncertain, but the component relationship is consistent with the meaning of muteness or muffled vocalization.
A mouth (口) that tries to make sound (音) but only manages a choked sob. Picture an infant's mouth open, but only a muffled cry comes out.
For イン, imagine an infant sobbing inside a quiet room: the 'in' sound of 'inside' cues イン, and the muffled crying fits the meaning.