#It depends on the where the point of silence was placed
Silence requires you to center the spell on a:
point you choose within range
How Resilient Sphere works, is dependent upon where that point is.
##If the point is inside the sphere, the wizard is silenced. The point is within the resilient sphere and therefore the sphere wouldn't be able to stop the spell effects because it's already inside.
##If the point is outside, the wizard is no longer silenced. Resilient Sphere states:
Nothing--not physical objects, energy, or other spell effects--can pass through the barrier, in or out, though a creature in the sphere can breathe there.
If the spell effect's point of origin is outside, the sphere actively prevents spell effects from passing through. The inside of the sphere would be a safe bubble from silence.