3

Sentence 1: 先生、この歌をお聞きになったことがありますか。

I thought it can just be
Sentence 2: 先生、この歌をお聞きになりましたか。

Is sentence 2 wrong? If it's not, what's the difference in nuance between those two?

6

Not wrong. The difference is same as in English.

Sentence 1: この歌をお聞きになったことがありますか。

Sentence 2: この歌をお聞きになりましたか。

These can be translated to

Sentence 1: Have you heard this song?

Sentence 2: Did you hear this song?

The first one puts emphasis on the experience and the second one on the fact (not so long time ago).

It is natural for 先生 to answer "Yes, when I was 5 years old." for the first one, but this answer sounds strange for the second one. If 先生 answers "Yes, last week.", it sounds natural for both.

4

The two sentences in your example have slightly different meanings.

Sentence 1: 先生、この歌をお聞きになったことがありますか。   

You might say this to ask the teacher if he/she had had the experience of hearing the song in the past. In other words, "Are you familiar with this song?" or "Do you know this song?"

Sentence 2: 先生、この歌をお聞きになりましたか。  

You might say this to ask the teacher if he/she had simply physically heard the song with their ears. So, maybe you're playing a tune and before the first bar is finished you quickly stop the music to ask the teacher if he/she has heard what that you were playing that particular song. Sort of like, "Did you hear this song?"

Quick Summary:

Sentence 1: 先生、この歌をお聞きになったことがありますか

Have you heard this song before Sensei?

Sentence 2: 先生、この歌をお聞きになりましたか

Did you hear this song Sensei?

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