occasionally students who are interested in music ask instructors for how a double ended queue could be useful in the music industry.
This is a rather unusual situation and I'm surprised it arises for you often enough to ask about it here. You might want to elaborate more on why this particular question comes up so often (I'd expect it to come up, say, once in a teaching career). Do your culinary students ask where double-ended queues ("deques") show up in that field?
If there's no obvious application you can think of for deques in music, it's OK to say "there are no obvious applications I can think of for deques in music" rather than scraping around a mostly empty barrel and stretching the truth to come up with something.
Linked lists in general are low-level data structures primarily used in systems-level applications. Double-ended queues are even more specialized. They're basically unnecessary for most day to day, business application-level development. Most of the time, a simple array is sufficient, and most languages don't have deques built-in to the standard library (Java, Python and I think C++ and C# are exceptions that come to mind).
With that in mind, the operating system running your musical applications is very probably using them, as well as potentially the software running whatever audio system you're using, but that's low-level and perhaps unsatisfying, since the data structure is probably not doing anything obviously musical here.
Scoping appears to be necessary. "Music programming" is a large expanse ranging from extremely low-level DSP engineering all w to extremely high-level music creation applications like Audacity, Lilypond, Ableton, Cubase, Reaktor, etc. Middle-level applications like Max/MSP, Tidalcycles and Supercollider exist as well. Zooming out to "the music industry" is even broader, and linked lists and deques surely appear in operating systems of people working in the music industry (again, unsatisfying and vague, probably not what the asker wanted to hear).
If your students are asking about music-making techniques that could use linked lists or deques, you could probably treat a linear song structure as a sequence of linked nodes, but this isn't too helpful or interesting (and would probably involve duplicate nodes). Deques can be used for rotating purposes, which might imply a looping structure of some sort, but since this is so unusual and we're breaking a sweat to come up with something, we'd better just admit it. An array would be just as useful for storing, looping and forward/reversing a musical piece, with the bonus of constant-time random access. A deque is appropriate when you want to dequeue or prepend nodes to the front of a structure in constant time.
I'd suffice to say that deques are a fundamental data structure in the low-level systems world, and then ask the student which level of abstraction and what domain they're interested in (it could be they don't even care about music production, and just want to know whether a deque could be used in a playlist app, or something like that).
When a strange, overly-broad question arises, it's important to follow up and ask for clarification to understand what prompted the question and determine the motivation of the asker. Once the scope is appropriately refined and the intent is obvious, a satisfying answer will be much easier to provide.