John.
Good idea to only fix what's broken because renewing parts at random could cost you as much as a new car. With so little information to go on there are dozens of possibilities, so let's try to get some specifics.
[1] Can you feel any vibration when the noise starts, and if so where? (Floor, steering wheel, pedals.)
[2] Does the noise change when you fully open and fully close the throttle at 60 mph?
[3] Have the road wheels been balanced recently?
[4] Does the noise change as you turn the steering wheel? (I appreciate you can't go full lock at 60 mph so don't turn further than is safe.)
[5] Has the car been serviced according to the schedule, particularly regarding engine belts, water pump, etc?