I see on the Aussie ebay auctions of American tube analogue (ie, non-digital) clock radios. Sure, the mains voltage is easily enough converted from 240 to 120VAC via a step down transformer, but what about the mains frequency? America uses 60Hz and Australia uses 50Hz. Most all American electric clocks use a synchronous motor for the timing, and they expect to see 60Hz. On 50Hz, these clocks would take 72 minutes of real time to indicate the passage of one hour. So do Aussie collectors of these clock radios: a) not worry about it? or b) change out the Telechron (a large percentage of clock radios used Telechron movements) module in the clock mechanism with one designed for 50Hz? or c) use some form of mains frequency converter to get 60Hz (that would be non trivial)?

I'd have the inverse problem with an Aussie clock radio here in the USA.

The most popular electric wall clock here is Smiths and their mechanisms also found their way into clock radios and car instrument panels way back then.

You are right that due to the motor being syncronous that mains frequency has to be right. I think the cheapest way of running an Australian clock in the US or vice-versa is to purchase a small inverter from the country the clock comes from and then power that from a 12 VDC power supply.

Jaycar Electronics has dozens of inverters for sale with a 50Hz output. I have two that I use for camping and can attest to the quality and I am sure they will post to the US.

One thing to remember - the inverter's output must produce a sinewave. If you use a modified squarewave unit (the waveform looks like a staircase) the clock's motor may fail to run at syncronous speed and may even overheat.

I have a nice little 110v Admiral US clock radio, just set it to Internet time and will let you know how it keeps time.
Admiral Clock Valve Radio
Back again, did some calculations, 60Hz sychronous clock motors run on 50Hz will lose 12 minutes an hour.

N=120 x f
-------
P
You have a 20% difference. So a motor doing 200rpm on 50Hz will do 240rpm on 60Hz.
Mine did when I set the time, I usually have this radio on my display shelf.