A HARD question (1 Viewer)

[co6]

This is a question from last year's physics olympiad. When I actually had to do it last year I couldn't even attempt it, but yesterday I saw it and was overwhelmed by an urge to conquer the unsightly bastard.

One day later I've got 5 sets of solutions and I have no idea which, if any, are correct.

Hoping someone can help!

 

[wrxsti]

May god have mercy on us all......

 

[TesseracT22]

i think i might have found a way to do it but ill just check first , is the answer to part b)

1.75*10^(-17) Hertz?

 

[co6]

i think i might have found a way to do it but ill just check first , is the answer to part b)

1.75*10^(-17) Hertz?

Yeah I got 1.736x10^-17, 3.472x10^-17, 5.20810^-17hz the first time I did it. You let k=1,2,3 etc. right?

For comparison, two of my other approaches yielded..

5.527x10^-18Hz, 1.105x10^-17Hz and 1.658x10^-17Hz

5.52734x10^-18Hz, 5.52972x10^-18Hz and 5.53211x10^-18Hz

 

[TesseracT22]

uhh no what i did was find the dimensions of the galaxy using the first information.
Since we have a sphere you can work out its volume and then its radius

for the volume you use the sum of all the mass in the galaxy(the stars) and the density to find the volume.

from the radius you get diameter and obviously the wavelength cant be longer than the diameter and the longer the wavelenth the lower the frequency

and longest wavelength = 2radius

using the info you can get an equation relating f to lambda and then you just plug in 2radius into lamba and you get f

most of the info is given and you need to manipulate it i think.

 

[TesseracT22]

btw what level of the phys olympiad was this in, NQE?

 

[co6]

uhh no what i did was find the dimensions of the galaxy using the first information.
Since we have a sphere you can work out its volume and then its radius

for the volume you use the sum of all the mass in the galaxy(the stars) and the density to find the volume.

from the radius you get diameter and obviously the wavelength cant be longer than the diameter and the longer the wavelenth the lower the frequency

and longest wavelength = 2radius

using the info you can get an equation relating f to lambda and then you just plug in 2radius into lamba and you get f

most of the info is given and you need to manipulate it i think.

Yeah this was from the NQE. The "syllabus" they gave us just said we had to know about waves without going into specifics :burn:

But yeah that's what I did for one of my approaches, fit the wave into the galaxy's diameter.. If you'll forgive the messiness of the first two pages, this is what I did for my last two attempts:



From the description I deduced that there'd be a field line around the circumference of the galaxy, and so the Alfvén wave could be imagined as a circular guitar string (bear with me here ). I then assumed they had to be standing waves to set up some kind of restriction lest I ended up picking big numbers out of a hat.

The first two pages show one attempt, while the page after was another one using some results from the previous two pages (it's not like I'm being examined this time so no reason to show myself how to figure out the size of the galaxy etc.).

 

[TesseracT22]

Yes well the thing about olympiads is that they arent testing how well you know a syllabus(HSC).
It's actually how well you can think and play around with what they have given you and also olympiad problems can be varied alot so you can't really make an outright detailed syllabus.