Learn French: Une sirène a sonné pendant que la police cherchait le voleur. - A siren went off while the police were looking for the thief.

This is the core pattern of this lesson! The imparfait is used for the ongoing background action: la police cherchait means the police were already in the process of looking. The passé composé is used for the sudden, specific event that happened in the middle of that background action: a sonné means the siren went off.

In English we say 'the police were looking' (plural). Why is the French verb singular (cherchait)?

In French, la police is a singular feminine noun. It is a collective noun, so it is helpful to think of it as 'the police force'. Because it is singular, it takes the il/elle form of the verb.

Could I just say pendant instead of pendant que?

No, because of what comes next in the sentence. Pendant means 'during' and is followed by a noun (like pendant le repas, during the meal). When you want to say 'while' and follow it with a subject and a verb (like la police cherchait), you must use the phrase pendant que.

I usually think of sonner as 'to ring'. Is it the standard word for an alarm 'going off'?

Yes! Sonner literally means 'to sound' or 'to ring'. It is the standard French verb used for anything that makes a ringing or blaring noise, including alarms, sirens, telephones, and doorbells.