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I think they're referring to the fact that it sends the pulse once per second. Could have been worded differently.

"each second" perhaps.

Yes, it should have been translated as "once per second." Perhaps the "每秒一次"(once per second) was abbreviated to "每秒"(per second) somewhere in the news report.

Maybe it's an accelerating frequency, like a chirp? :)

Yep, but they did get it right a little further down the article.

But what is the monitor an acoustic wave--isn't it a radio signal?

No, it's an acoustic wave. Salt water is a good conductor of electricity, as such only ultra low frequency radio has any chance of penetrating more than a few feet, and the antenna needed to pull that off is prohibitively large for an aircraft.

Radio doesn't penetrate water well. It also emits sonar pings for the case where it's in water.