Interview for Physical Natural Sciences at Cambridge

I actually wrote most of this the day after my interviews but my Non-Disclosure Agreement (which ends tonight) prohibited me from posting this. So now in the spirit of full-disclosure, here’s how my interview went.

Applying for PhysNatSci at Corpus Cambridge means you get a choice of being considered by the head of Physics or the head of Chemistry. Considering my utter ineptitude when it comes to organic Chemistry I naturally chose Physics which meant I had to take a Physics test as well as have interviews (the chemists didn’t). Good thing is I didn’t have to sit the TSA…

Corpus Test [60 mins]. Non-calc.

Apparently ‘nobody finishes all the questions’ but it was well within the capability of most people in our set to do this in the time, and I did. I wouldn’t say 1 question every 6 minutes is over-ambitious; it’s probably just the college trying not to freak people out. Dr Sutherland said I did very well in the test and we didn’t discuss any of those questions (which they did discuss for the previous guy – I couldn’t help but overhear a bit). M = Maths, P = Physics.

M1: Estimate sqrt(101) to 4sf

M2: x+y = xy = 3. Find x^3 + y^3.

Was quite surprised with this answer!

M3: differentiate x^x and x^(1/x)

M4: Sketch y = x/(x-1)^2 and y^2 = x/(x-1)^2

Had time at the end so I found the turning point. Did this my personal way by dividing top+bottom by x and finding x coord of turning point of the bottom. I just dislike the quotient rule I guess. Too messy.

M5: A generalised Fib sequence is given by F(0) = 1, F(1) = a, F(n)=F(n-1)+F(n-2). For what values of a is this a geometric progression? Find sum to infinity.

Wrote answer as a = phi or a = phi – sqrt5. Latter converges.

M6: Sketch y = tan(x) and y = arctan(x) on the same axes. Hence or otherwise, find the integral from 0 to 1 of arctan(x)

For some reason that I still do not understand, I decided arctan(1) = 1 (and missed it when checking) so integrated with incorrect limits and used the wrong area of the rectangle. I hope that didn’t make me seem too extremely retarded.

P7: Sketch acceleration-time and velocity-time graphs of a parachutist jumping out of a plane, opening the parachute, then landing safely on the ground.

P8: Water is placed in a sealed vessel. What would happen to the pressure if all forces between water molecules were to disappear?

I wrote an expression for this using PV=nRT then converted n/V into (water density)/(molar mass of water in Kg) so P is only in terms of constants and the temp. But I overheard the end of the previous interview – they were discussing this question – seems like all you had to say was ‘P goes up because intermolecular forces are attractive’ (neither of which I actually wrote – damn).

P9: Light inextensible strings, masses forced to move up-down. Find a as a function of x and sketch the graph.

I panicked when I got a horrific 2nd order ODE that I couldn’t solve then realised I didn’t have to solve it (since I had to find a(x) not x(t)). I was surprised to find a was infinite at x = l but it kinda makes sense considering tensions.

P10: Force F pushing againt 5 blocks: F -> ■■■■■. Acceleration a to the right. Draw all forces. What is the resultant force?

P11: The radius of the Earth is about 4 times the radius of the moon. What is the ratio g(earth)/g(moon)?

Used Gauss’ law for gravitational fields, complete with surface integral and symmetry argument to evaluate it. Thank you CAPS!!

Went out before and after Corpus dinner (which was excellent) and didn’t actually get to sleep until after 2am – I’m not great at sleeping in unfamiliar rooms/beds. I did manage to get this rather nice photo out of my bedroom window using nothing but incredibly steady hands and a ridiculous ISO:

Woke up at 8 for breakfast (of which I ate a disproportionate amount; again excellent) and spent the morning extremely unproductively in the JCR – the freshers who were helping put on History Boys… Got lunch (if I get in I will relish every meal), had an enormous cup of coffee and braced myself.

Corpus Interview 1 [30 mins, Dr M Sutherland and Dr S Bohndiek (latter from another college)]

1. Sketch the graphs of x^2 + y^2 = 1 and x^100 + y^100 = 1.

Interviewer said this was an easy warm up.

2. Show that z_n = exp(-x^2/2) is a solution to d2/dx2 (z_n) + x d/dx (z_n) + (n-1)x = 0. [something like that. No idea where n came from.]

Totally screwed this one up. It was a really trivial question – literally plug in the answer – but by the time I’d finished differentiating the thing several times I forgot where I was trying to get to so didn’t complete the final part – subbing it all in! From this point on they must have thought I was stupid and gave me easy stuff which really sucks.

3. Ice sitting in a glass full to the brim of water. The ice melts. Does the glass overflow? What will happen if the Arctic ice melts? Does this mean sea levels will not rise?

4. Estimate the change in sea level if everyone in the world went swimming in the sea at the same time.

Assumed Earth’s surface is flat without saying so – oops. Got about 10^-6 metres.

5. Integrate sin(x)sinh(x).

First talked about parts – and explained why it doesn’t work with sin(x) * sinh(x), realising (mentally) the problem reduces to 0=0 after two integrations by parts. Tried writing sinh(x) as e^x – e^-x then doing parts on each bit – works – can let I = integral and solve algebraically after doing parts twice; standard trick. I explained this doesn’t work for the first splitting because you get +I on both sides of the equation whereas with the second splitting you get +I on LHS and -I on RHS and the equation can be solved. Interviewer implicitly didn’t let me write anything down (“don’t do it – just talk about the method”) until they asked “how much do you know about complex numbers?” and my face must have lit up and I immediately said de Moivre and got the answer. Perhaps should have made it clearer that I hadn’t done it in school (but just happen to know of it and find it cool) since I needed to be ‘reminded’ whether it was cos + i sin or sin + i cos.

6. e^(i pi)

Awesome I got asked this :) I identified it as Euler’s identity and showed it from de Moivre.

I didn’t feel great after this interview – still kicking myself over being such a complete and utter retard for that differential equation / normal distribution question. People get executed for that sort of stupidity in China. Maybe that’s a good thing – cleans out the gene pool (much like Darwin awards).

Corpus Interview 2 [25 mins, Dr P Beattie and Dr P Cicuta]

At first the interviewer sat me down on this really uncomfortable chair which creaked a lot and I nearly slid off (like Hammersmith bus station) and said Corpus has 2 interviews for second opinions and in case one interview goes badly (so hopefully I managed to redeem myself).

1. What have you read about Quantum Computing? What problems do researchers face? How are they attempting to overcome these problems?

Talked about qubits and mentioned unit vector idea, introduced ket notation, talked about quantum parallelism but didn’t get onto Shor’s algo. Main problem is quantum decoherence. Evacuate experiment, cool with either other large ions or lasers. I could have gone on for a (very) long time but didn’t…

2. You play the violin [yes]. How would one work out the frequency of a string vibrating? Would a change in air pressure affect this frequency?

I remember seeing v = sqrt(T/(linear density)) somewhere once before so used it.

3. A standing wave is set up in a tube full of air sealed at one end. Draw the standing wave. What is the frequency of vibration? How would a change in air pressure affect the frequency? If an entire orchestra were playing and helium were pumped into the room, what would the audience hear?

Wind instruments go higher, string instruments don’t. Orchestra would probably get a bit out of time (brass and wind tend to be slightly out of time unless they correct for time delay of sound getting to them so their correction timing delay would be wrong) but I didn’t mention this.

4. What is the frequency ratio of an octave? a fifth? If you go up twelve fifths, would you go up an integer number of octaves? [Not quite]. How does the piano overcome this?

2x, 1.5x. (3/2)^n is never an integer. Well-tempered klavier; semitones are a lie!

5. Estimate the fuel effiicency of a jumbo jet and a car [litres per (passenger mile)]. Comment on your answers.

They seemed happy that I guessed the unit right but I couldn’t estimate the volume of fuel a jumbo jet would use – I attempted a really unintelligent method of getting at the answer by comparing the time it takes to fill up a jumbo against that to fill up a car. Interviewer suggested just saying it takes one tanker to fill a plane.

Turns out efficiencies are about the same, but I pointed out the two types of transport don’t exactly compete – you wouldn’t take a jumbo for a journey conceivably doable by car!

6. A yo-yo and a rock are dropped simultaneously. Which one accelerates faster? Why?

First the idiot in me used the extremely clunky and inelegant moment of inertia argument and obtained an expression for linear acceleration after drawing a force diagram. I offered to work out I for yoyo by integrating but interviewer said don’t bother. Interviewer then asked me whether there’s an alternative argument. I said energy. I tried to make it clear we hadn’t done circular motion properly in school yet but I said I was guessing formulae by comparing with linear stuff (esp. rotational energy E = (1/2) I w^2) and he seemed to agree with me. Ironically in the very mechs lesson I missed to go to interview AJM taught this stuff.

Dr Beattie said it was very good at the end – nice feel-good to end whole experience with which put me in a good mood for the rest of the day, though possibly it was just a horrible mind trick to give failed candidates a good feeling about themselves. In each one both interviewers alternated asking questions (they were very deferential about who asked the next question!)

Overall – despite the illusion of having not failed too much, which made me think it had all gone swimmingly, thinking back, there wasn’t a single hard question which was really quite concerning – nobody doing both physics and FM at SPS would have found any of that remotely difficult. Hearing what other people who also had Cambridge interviews said, it seems like everyone else got an opportunity to show off (bouncing balls losing energy at each bounce, infinite ladder of resistors linking to the golden ratio etc.) whereas I may well have come off as a stupid exam-factory-drilled robot who can only do bog standard questions on topics. I also didn’t get to talk about stress-energy tensors, semiclassical gravity and black stars (cf. one of the most awesome SciAm articles published recently) which was also annoying. Both interviews were friendly – the second was extremely so, and the first possibly a little less; both were formal and at desks – no armchairs/sofas etc.

The plan: if they gave me easy stuff for the reason I think they did, I’ll go to Stanford whence I have an offer… And since I am an avid rock climber t’would be all the more awesome.

Most of the other people applying to Corpus (nobody that I know of from SPS or SPGS or indeed any other school I know well) said they found the test and interviews difficult – but as Matthew pointed out, apparently a Game Theory analysis suggests the strategy that if you’re weak, act strong and if you’re strong, act weak. Considering everyone was applying for hard sciences at a top university it wouldn’t surprise me if they were mostly just good game theorists in addition to good scientists.

I get the decision letter (and possibly email) tomorrow. Eep.

4 Responses to Interview for Physical Natural Sciences at Cambridge

  1. Ketan says:

    haha, you are too negative. they probably gave you easy questions because they had already decided to take you. if you got a “so good we wont discuss your test responses” then they were probably just giving you a relaxing time cause you deserve it. :)
    tell me when you get th letter…

  2. That’s a lot of questions. Good times. Also Ketan, have you read Outliers?

  3. Will says:

    “bouncing balls losing energy at each bounce” – did someone apply to Emma? I got that one. And it’s no harder than what you got asked…
    I doubt anyone comes out without having done something stupid – I tried to do dimensional analysis (to find the string frequency, coincidentally) by adding.
    Similarly surprised by xy=3 question!
    I have every confidence that I’ll be seeing you next year.

  4. Bryant Tan says:

    Will: I think the bouncing balls one might have been Pembroke. Or Queens. AJM had actually done that question with us a couple of weeks beforehand. Love these coincidences :)

    Farhan: I believe it was that very book that led him to do a big project for apposition (!)

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