Translation:The students have difficulty hearing the professor.
I have been wondering the same and checked a few pages. It seems that in Norwegian "å vente" can mean: wait, await, anticipate. There are several ways in which it connects with other words in the sentence.
You can have no "follow up", so sentences such: I am waiting (Jeg venter), Can you wait here a few minutes? (Kan du vente her noen minutter?), Wait and see (Vent og se)
You can have a noun after and then you need to use "på" after, such as: I am waiting for you (Jeg venter på deg), They are waiting for the ambulance (De venter på ambulansen)
You can have a verb after and then you need to use "med": Jeg venter med å rydde til morgen, Jeg kan ikke vente med å snakke med ham.
There are more complicated use cases that I found such as: Middagen venter! (The dinner is ready, it's "waiting"), You can expect ("anticipate") me at 6 (Du kan vente meg klokka seks)
I'm not Norwegian so it would be good to have some confirmation from a native :)
It looks good to me! :)
In the sense of anticipating/expecting it can also be used with a noun after it without a "på", but you're correct in saying that it would require a "på" if the meaning is "to wait".
General/Impersonal statements about anticipation/expectation are often prefaced by "Det ventes...", which could translate to "It's expected to/We're expecting/You can expect.." depending on the context:
"Det ventes regn (/å regne) i morgen."
"It's expected to rain tomorrow."
in English, a 'teacher' is anyone that teaches, and that includes professors, mentors. Even a teenager that teaches piano every week after school is a 'teacher.' a 'professor' is usually a university-level teacher, maybe someone that holds lectures or seminars. Their role is more academic than, for example, a primary school teacher, and you will often act more formally towards them than other types of 'teachers'
Australian here: Yes! It sounds more polite than "I can't hear" or "It's too hard/difficult to hear", and is the proper way to convey that message to, for example, your professor, co-worker, or boss.
To our friends, we would probably just say "I can't hear you," or "I can never hear what you are saying", or something similarly direct.