didn't notice you are/were studying

I'd go with were.

I's also take out the "this" or the "the" in the radio sentence.

"Is the radio bothering you?"

"Is this radio bothering you?"

Thanks. Dlowan.

It was a careless mistake; 'the' should not have been in the sentence.

The word to use is 'were' in keeping with the tense of the sentence, the past tense.

Also, in the second sentence, if you were asking about one radio you would use the word 'the', singular. You would use 'this' if you were asking about one radio out of two or more radios, 'this' radio not that one, or those radios. This is in accordance with American English grammar.

Thanks, InfraBlue.