Radio waves behave in interesting ways. Oftentimes, when an FM radio signal bounces off a building or mountain, it will change frequency and create a "ghost station". If you tune around the dial slowly, you might notice a faint station that when tuned a bit more will fade, then come in really clearly. It's possible you might be tuned to a ghost band if the tuner is analog (using a wheel rather than pressing buttons). Otherwise, if you see a little black or white wire coming from the back of the radio, find a way to tack this to the wall vertically - the straighter and higher, the better. This is a cheap external FM antenna that is often built into clock radios.
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I agree with the others, mostly. The internal antenna may be disconnected or just pointing in the wrong direction and you are tuned to a weak station. Tune to a stronger station and that should go away. Or turn the radio a little until the station comes in stronger. Your hand is acting as a reflector or antenna.
Agree with Nfarrow. Look for a plug or screw on the back that says "Antenna" or "Ant" or has an antenna symbol, which looks like a pole with a triangle on top. Put on 1-2 feet (0.3-0.6 m) of wire. Wire can be insulated but make sure end you attach it isn't.
Do you see an, “antenna” on your clock radio? I bet not so the reason is because it’s using the ground of the unit it’s self and when you touch the clock radio, it uses you as an antenna. At lest thats what I think. LOL