lc99 said:
So i have a question. In terms of difficulty, how difficult is this question for an exam?
I think it's easy, but it's interesting, because we have different perspectives on this topic.
lc99 said:
They will differ by the number of antinodes (n)
Honestly, I can never remember which are nodes and which antinodes! The nodes of Ranvier are the unmyelinated bits of nerve fibre, so I guess nodes on the string are where there's no transverse displacement. But if it was important for a question I might well look it up to check before answering.*
Here I'd thought to help you by getting you to say 30, 60, 90, 120, ...Hz, differing by 30 Hz, the fundamental. But even though I asked about frequency, you thought about wavelengths.
When I first saw the question, 500 Hz and 600 Hz as consecutive harmonics meant 100 Hz fundamental (as Haruspex said) and then I'd have had to think a bit about what that meant for the length of the string. I don't actually know the formula you quoted! (Another thing I would have looked up, though I might have been able to work it out, because they're all the same really.) Though, as you found, we don't need it.**
But it reflects a difference, not so much in understanding of physics, as view of the world. I see a vibrating string and think of frequency, like a guitar string. If I press my finger on a fret, the pitch or frequency is higher and that's what I'm thinking, not that the string or wavelength is shorter. You, not unreasonably, look and see nodes and thus wavelengths.
I also use old fashioned radio a lot, where frequencies are the defining characteristic. Wavelength is a bit of a moveable feast that we talk about in round numbers, but only pin down when we need it in specific situations. Most people have no need to think of wavelength or frequency if they use radio, because it's all channels and the rest is hidden away by the computers that control the equipment. Harmonics there can pop up all across the band and they don't tell you whether they are the 5th, 6th or 1739th. But the spacing tells you the fundamental frequency, so, maybe, where it's coming from. This is the sort of experience that creates the intuition I benefited from here.
So all questions are going to be easier for some people and harder for others, because we all have different experiences. Either way, I'd rate this as easy physics, because waves are a core topic and the maths is very basic.
* Nodes: it just occurs to me that you might be better off thinking of internodes, antinodes or bumps, rather than nodes. The fundamental has one bump, the 2nd harmonic two bumps, the 3rd has three bumps etc. With nodes, you always have one extra (or one less if you don't count the ends.)
** I'm never sure what PF means by "relevant equations". Here you seem to have picked a formula you thought was relevant before you started, then found it not useful (albeit still relevant?) Maybe you are supposed to fill this in when you've finished, with just the formulae you used?
