My horn no longer works and makes a soft bzzzzz noise when pressed. Is it my relay? 68 442 with 3 spoke sports steering wheel.

 

My first guess would be the horn itself or the ground it gets to the body.
Try substituting a known "good" horn in the circuit.

 

Check the CSM. There's a whole protocol for the horn. Just did it myself

 

The horns on my 442 sounded like dieing geese. I took them off and replaced them with parts store horns...BINGO! The originals sounded like miracas because they had just disintegrated on the inside. You never know....they are 45 years old after all.

 

Before condemning the original horns, try a slight tweak on the current adjustment screws on the horns themselves.
Try 1/10 of a turn CW first. If not go back to original position, then 1/10 of a turn CCW.
Sometimes the internal contacts get corroded and need a little more pressure from the screw to make it work.
Just make not of where the original position of the screw is first!

 

All I have ever gotten from twiddling with the adjuster is a different horrid noise. In MI they rot away inside. When the '85 needed horns I went to the local yard and got Cadillac horns. Now it sounds like a huge car of course.
To fix your horns follow the CSM procedure.
Your steering wheel contact has to make the relay actuate, which sends power to the horns. Not much to it. Most troubleshooting can be done at the relay which will show if the issue is towards the steering column or towards the horns. Or, the relay itself.

 

And I have fixed several with a slight tweak of the screws.
Just something to try before chunking them or even removing them.
A slight tweak, not much. I fixed both horns on a 2005 kia this way also.