Yes that will be the cause. I had the same problem with my 1957 oval as a previous owner had converted it to 12 volt and left the 6 volt wiper motor in place. It ran so fast that it threw a wiper arm off the spindle and into the road!
I fitted a dropper unit made and supplied by Peter Good of Volksgoods. He makes one especially for wipers and it works superbly.
www.volksgoods.co.uk
Peter has recently rebuilt me a 6 volt generator, so before the car comes out of hibernation in 2009 I'm converting it back to 6 volts.