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Now if only cellphones included an AM receiver. And if only modern radios didn't often strip the AM band out of their devices anyway...
How big an antenna would a cellphone with an AM receiver need?
If I remember correctly, cellphones with radio receivers tell you to plug in headphones whenever you're tuning in. My guess is the headphones cables act as the antenna.

[Edit: TIL AM stations seem to transmit at frequencies way smaller than FM]

AM is around 1Mhz so that's a 300 meter wavelength. For a half wave dipole (basic high efficiency antenna) that's 150 meters of wire. A vertical antenna (like on your car) using a ground plane as the other end of the dipole would be 1/4 wave so 75 meters.

All this said, AM @ 1Mhz propagates very efficiently regionally and they broadcast at insane power levels so efficiency on your end isn't that big a concern if you're within a couple hundred miles of the transmitter. You can get away with a meter long antenna just fine.

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The press release indicates that they're using RadioSAFE:

http://www.theradiosource.com/products/radiosafe.htm

> RadioSAFE Broadcast Systems have the capability of staging hundreds of preplanned safety messages that can be selected locally or remotely at a moment’s notice and updated minute by minute. Programming can be performed at the station or remotely via telco or UHF/VHF transceiver or by LAN/WAN if optioned. Redundant levels of message control are provided in the RadioSAFE design.

An antenna upgrade is offered:

http://www.theradiosource.com/products/antenna-hpr0990.htm

> 300 Watts, 470-1800 kHz, 20+ Mile Radius Range

Various warnings are noted about requiring an FCC license beyond certain transmission power thresholds.

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That's one hell of an inefficient antenna. At a ~1MHz center frequency it's basically just a dummy load (resistor) that happens to radiate a little. 300 Watts at those frequencies on a long run of speaker wire with a matching transformer/unun at one end could get you 100s of miles during the day and 1000s of miles at night.
Speaker wire generally degrades in sunlight, so that might not be a valid comparison for the "disaster-resistant permanent installation" market.
Weird, I wonder why they chose to build this? Is this sort of an "end of the world" style system, where it's assumed cell phones, internet, and other forms of communication are already failing?

Here in Maine we already use AM radio (I think 1600 or so?) to broadcast short range info about situations that occur on the interstate, using the mentioned Travelers Information System. Next time I'm in my car I should verify I can receive AM radio signals

There are non-end-of-the-world scenarios in which this is useful. For example, during the California wildfires, landline and cell service was down. During the Chicago Marathon, the crowding was so great that cellular service in downtown was very spotty, and they needed Ham Radio to carry on medical emergency communications.