Solution 1:

There's no difference in meaning between "without xxx" and "with no xxx", but the former is far more common. For example, "walked with no haste" gets only 3 hits in Google Books, whereas "walked without haste" gets 5310 (an extreme example, but the preference is always there).

The other main difference in usage is we tend to avoid "with no xxx" with gerunds (verb +ing). (Note how "with no caring" virtually "flatlines" on this graph).

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Solution 2:

I would say that the "no x" formulation is a more emphatic expression of "without x". "Without" expresses the importance of x in a negative fashion, while the "no x" expresses it affirmatively...the former expresses (merely) that x should not be present, while the latter expresses the positive absence of the existence of x.

Overall, it's pretty subtle.

Solution 3:

Although there is very little difference in the OPs particular example, there is, in fact, a very significant difference!

There is little difference between 'without water', and 'with no water'. Without and with are both prepositions. When we are using 'without X' to mean there was no X at all, there is little difference in meaning between this and 'with no X'.

However, we cannot always use 'with no student', to replace for example 'without a student'. Sometimes we can use a to mean a specific item that is being thought of by the listener but is not identifiable to the listener. For example, if we were on a coach tour and Bob hadn't boarded and the coach left without him, then we could say:

  • We realised we'd left without a student.

but we could not say:

  • We realised we'd left with no student(s).

This would mean there were no students on the bus.

Really this is not quite the same thing grammatically as in the 'without sound', 'with no sound' example. We have replaced a with no as well as replacing without with with. The word no is a determiner. Determiners are words like a, the, some, any, this, that.

We actually cannot replace without with with no if the noun phrase already has a determiner:

  • without the book
  • *with no the book
  • without some help
  • *with no some help

The meaning of the phrase will also change if there is a number in determiner function:

  • without two friends
  • with no two friends.

The reason that this doesn't matter in the Original Poster's example, is that sound is being used as a non-count mass noun, and so doesn't need a determiner in the first phrase.

Hope this is helpful!

Solution 4:

Mayhap others will have other differences, but I only can point out one difference in usage.

In the following sentence:

He achieved this with no mean effort.

"Without" would have a different meaning. "With no" here has the meaning that the fellow put a lot of effort. "Without" couldn't have been used here.

That's the only difference I could point out.

Solution 5:

With no is the common usage in American English. Americans say, "I want water with no ice" rather than without ice, though both mean the same thing.