340 3" exhaust unbearable

I Think that is called a chassis excitation. I had that on a 69 Barracuda 6 cylinder at exactly 50 mph. The car was impossible to spend any time there. 50mph with 2.76s and N-50s(don't ask) was just about 1800 rpm. My solution was to not drive 50.That was 1977, and I was newly married. She had the furniture and apartment. I had wheels, and was extraordinarily handsome.lol
My chassis excitation wa s caused by the tires. It had not done it with the previous set.It was just as you describe except at speed.
"heavy heavy low WHUAH WHUAH WHUAH WHUAH WHUAH !!!!!!!!"
It went up into the seats and steering column, and pounded my eardrums.