Steamship officers/sailors checking their chronometers using wireless?

I've read that, during the steamship days, ships' officers had the ability to regularly check the accuracy of their chronometers even while away from their home ports. I know that various cities with naval observatories would announce daily time checks. But I do have some questions:

1)Would the people manning the observatories send regularly scheduled messages over telegraph lines to announce when local noon was?
2)How did the radio operators coordinate the relaying of this information to the outside world?
3)Were ships' officers able to receive these time checks over the shipboard wireless apparatuses so they could check the accuracy of their chronometers daily, even while at sea?

Any answers would be much appreciated.