First of all, let’s be very clear about cycling and speed. There are bikes made for speed and bikes made for leisure. You can ride a race bike leisurely, but that doesn’t work the other way around.
Choose your weapon…
Speed wobbles are caused by a flaw in a bikes setup or due to a worn out component (wheel, headset, etc.). I ran into the latter several years ago, a worn-out, rusted headset.
Heading down a very nice hill near Lake Nantahala in North Carolina, I hit about 47-mph going down the straight shot when my bike started shaking violently from side to side. It scared the hell out of me… I was certain I was going to crash. But, while coasting, I placed my left knee against the top tube of the frame. This helped, but I was still heading toward a ditch at better than 40-mph… I placed my other knee against the top tube and squeezed the frame till the cavitation stopped and I safely stopped.
Once I steadied myself, I rolled on. I kept it below 45 on that bike until just this year. I’ve been beyond 55 on my Specialized Venge and that was a fantastic, stable experience. This last week I just took the Trek to 52 on that same hill, after a new headset, and it was a wonderful experience. In fact, on another hill with a posted 35-mph corner at the bottom, I was comfortable enough to take that at better than 40… and that was fun!
Speed wobbles happen when the bike develops a shimmy and that resonates through the frame until the shimmy, or flutter, hits a magic resonant frequency, it feels as though you’re riding on ice. You can’t control the bike, and it’ll be likely, if you don’t stop the bike or the flutter, you’ll crash.
The key is to put a force against the flutter of the bike frame. In my case, the knees against the top tube. This changes the dynamics of that cavitation, thus slowing or stopping the flutter, and control returns.
All one has to do is remember this when it happens to them.
Remember, if you ever experience the speed wobbles, clamp down on the top tube with your knees. It could save your 🥓.
Fit Recovery 
This is a very good tip Jim and I appreciate the explanation. I’ve seen riders in this position going down hills and been given the explanation it was for stability. Now I understand exactly where to put the pressure and why. Thank you!
Awesome! 😁