Dick Merchant wrote about using a noise canceling system for quieting
a blower.  It would work just fine on the noise coming out the exhaust.

There are several companies that make just such a device for the
air handling industry, and even one for a car (a bit pricey, though).
There are also similar devices that you can wear to listen to tapes,
etc., through headphones while mowing the grass.  A couple of friends
have them and say they work.  They are only around $100.  If you want
to try the idea, I suspect that a pair of these headphones would be a
good place to start.

It's a simple principle but a lot harder to implement than it looks.
It involves not only sound volume but frequency and phase of the sound
-- and it is position and feedback sensitive.  And there is another
problem:  What do you do about the noise that is NOT coming out the
exhaust or the tubing on the vacuum side?

The real problem is not so difficult that a carefully designed 'box'
for the blower can't provide an adequate solution.  In general, make
the box out of high density materials (MDF or HDF*) to limit sound
through the sides, soft mount the motor and the box and use sound
absorbing material to absorb the high frequencies in the box and the
air paths (with a few carefully arranged turns).  Don't forget to
allow for cooling.

At least you don't have a bunch of low frequencies from a motor
and bellows to deal with.

Craig Smith

* Maybe Baltic Birch plywood would be better since the plywood would
absorb more mid-frequency energy and probably not transmit much more
low frequency energy than the MDF.