I dislike these kinds of questions, because they’re usually posed at a point well before the wave equations are presented. At this point, you are largely working with verbal explanations and, as you point out, verbal explanations are much harder to pin down
What would the same question look like when presented in mathematical form?
At a quick glance I can’t see a concise way to express it.
That’s the point—to actually be precise you need both wave mechanics and statistical mechanics as background to even define the “speed” of a “sound” “wave,” the “temperature” and “pressure” of a gas, and how a gas gets “heated.”
At what appears to be this level of coursework, it should be something they’ve already discussed in class. Otherwise, it should be either asked with a lot more context, or as part of a discussion instead of on a test.
I’m assuming this is something like a high school level physics class, and that this specific problem hasn’t been discussed before the test. In that case I think it’s a sufficiently hard problem that if you’re going to ask it on a test, then it should be a multi-part series of questions that leads to towards the right mode of thinking. Maybe something like, “1) What happens to the average speed of molecules in an ideal gas when it gets heated up? 2) How, if at all, does this affect the speed of sound? 3) How, if at all, do changes to V and P affect the speed of sound in an ideal gas?”
What would the same question look like when presented in mathematical form?
At a quick glance I can’t see a concise way to express it.
That’s the point—to actually be precise you need both wave mechanics and statistical mechanics as background to even define the “speed” of a “sound” “wave,” the “temperature” and “pressure” of a gas, and how a gas gets “heated.”
So how instead should this category of questions be ideally presented?
At what appears to be this level of coursework, it should be something they’ve already discussed in class. Otherwise, it should be either asked with a lot more context, or as part of a discussion instead of on a test.
I’m not sure how to imagine ‘a lot more context’ for this question, can you provide an example?
I’m assuming this is something like a high school level physics class, and that this specific problem hasn’t been discussed before the test. In that case I think it’s a sufficiently hard problem that if you’re going to ask it on a test, then it should be a multi-part series of questions that leads to towards the right mode of thinking. Maybe something like, “1) What happens to the average speed of molecules in an ideal gas when it gets heated up? 2) How, if at all, does this affect the speed of sound? 3) How, if at all, do changes to V and P affect the speed of sound in an ideal gas?”