Remember that when the fan starts, the air builds up in the duct work before you get the full flow through the house and back through the return.
Suggested starting place is in your rectangular duct and return air work. Look on a wider section for tin that flexes in and out with the pressure and also by hand. Bracing may be needed there. On the wider sections, they sometimes bend creases that keep the tin flexed outwards.
Before your wife leaves be downstairs by the a/c and have her turn it on and listen. (Remember that you may have to wait for the air to go static and the duct to flex back again so it may not be something that can be duplicated with every throw of the switch.)