HiFi Quiz - vinyl record music reproduction. Who is the AOS clever clogs?

[Barry]

Harmonic? I thought you wanted to know the groove amplitude of the 10KHz signal, at -50dB relative to the groove amplitude of the 50Hz tone.

Assuming the record was cut with a constant-amplitude profile, then I would say the -50dB 10KHz groove amplitude is ~10um (i.e. 3200/(sqrt(10⁵)) = 3200/316.2 = 10.12)

[Oldpinkman]

But not too much precision guys - the idea was based on explaining to Mrs Sutton just how astonishing the engineering was , and pinched from Martin Colloms, who in turn pinched it from E B Meyer of the Boston Audio Society - so like I didnt specify the thickness of the paper on the dollar bills, or the impact of the elastic band between bricks...

I think most people struggle to think in numbers outside their normal frame of reference. I know I simply cannot get my head round the real numbers in the Universe when reading Brian Cox's book. Analogies like this just help get a perspective. Most people guessing at a trillion end up thinking "as high as the empire state building" or "mount Everest" as impossibly huge numbers.

I'll give you the real answer that was used in the analogy and just leave you to convert the scale. The vinyl deforms by about (!) one micron. A measurement which means nothing to Mrs S. My turn for a beer

[sq225917]

10.12 using your 3200mm example, (barry beat me to it)

I don't think too many of us willing or capable of doing the math are unfamiliar with the scales involved. Admitedly there's probably less that way inclined on this forum than most others.

[Oldpinkman]

10.12 using your 3200mm example, (barry beat me to it)

I don't think too many of us willing or capable of doing the math are unfamiliar with the scales involved. Admitedly there's probably less that way inclined on this forum than most others.

I'm sure you're right on both counts. It was to share the wonder with those not capable of doing the maths (me included ) that I thought the post was worthwile. There are quite a lot of comments on here from folk, who may not have been aware. I take it your answers are 10 microns or 1/100th of a cm or 0.1mm. The original example quoted by Colloms was 1.9mm, but (as I'm sure you know) your maths is correct and I think the variance comes from me trying to scale up the original reference which was 1Khz at 5cm/sec giving about 47cm lateral movement, and the RIAA curve characteristics. If it bothers anyone I'll find out for sure.

To address Barry's point - yes - that was the groove amplitude. It is typical of a frequency found in a violin harmonic (ie its way above the pure tones found on a piano - c8 is about 4.1Khz - and I know you knew that too, but its for the others we are sharing the love with) but its still a note you expect to hear - its a real note, but that pitch is only heard as a harmonic not a main frequency. (Cheez - I'm an apologist for Martin Colloms - I never, never, never thought I'd find myself in that role)
You all win the prize, and I am happy to buy you a drink any time we meet


The real point I was after was in a system where the arm sits 400 metres above the record, the stylus has to cope with tracking grooves as big as 3.2m and as small as 0.1mm or 2mm, when the stylus itself squashes the vinyl by about 3cm or 30mm - nearly 10 times as much as the low level 10Khz note (as typically produced by a harmonic from a violin).

Imagine what happens if a resonance on slightly loose bearings at the pivot point move the arm at that point by a micron or two and are amplified by a leverage effect over 6km to the cartridge body. That was the idea.

I think I'll stick to counting beans

[Barry]

Starting with http://www.vinylengine.com/turntable...ic.php?t=22894, we will assume the record is being played with a 0.3mil x 0.7mil elliptical stylus tracking at 1.5g.

The contact area with the groove wall is 40 (μm)² and the contact pressure on each wall is 26.52 10⁶ Kg/m² or 2.7Mpa. The deformation of the vinyl by the stylus can roughly modelled using the Hertzian stress formula for a sphere (the stylus tip) resting on an elastic half space (the record wall).

To maintain the same contact pressure, the radius of the spherical tip is taken to be 3.57μm

According to http://en.wikipedia.org/wiki/Contact_mechanics, the indentation is related to the spherical tip radius the contact force and the material properties of the two surfaces:

An elastic sphere of radius R indents an elastic half-space to depth d, and thus creates a contact area of radius

a = √(Rd)

The applied force F is related to the displacement d by

F = (4/3)E*. R^1/2.d^3/2

where

1/E* = (1-ν₁²)/E₁ + (1-ν₂²)/E₂

and E₁, E₂ are the elastic moduli and ν₁, ν₂ the Poisson's ratios associated with each body.

Since the elastic modulus of diamond is 1220GPa (some 400 times that of PVC), the effective elastic modulus E* is taken to be that of the PVC alone (for which a figure of 3GPa is assumed for the latter).

Doing the sums, the static indentation of the vinyl record wall by the stylus under 1.5g playing weight is calculated to be 1.09 10^-6m or 1.1μm.

The static pressure on the groove wall is 250MPa or 0.36 million pound/square inch!



However the operative word is static. Under dynamic conditions with a moving groove wall, Hertz’s theory does not apply. All one can say is the deformation will be considerably less due to the limited time any part of the groove wall is under compression.

[Clive197]

Haven't you lot got something better to do. For example, telling the wife, partner or significant other half that you are taking the dog for a walk but in fact going down to the pub and sinking a pint or two.
Boy it's warm tonight.

[Thing Fish]

Haven't you lot got something better to do. For example, telling the wife, partner or significant other half that you are taking the dog for a walk but in fact going down to the pub and sinking a pint or two.
Boy it's warm tonight.

+1

[Oldpinkman]

+1

Thank you both for taking the time out of your busy and important lives to express your condescension and superiority. I apologise for wasting your precious time with an attempt to provide a Brian Cox style analogy of the true magic of the physics and engineering involved in getting music from a gramophone. So - tell me instead about your designer kettle leads, and how careful alignment with the prevailing ley lines means I can achieve improvements in domestic audio reproduction I might otherwise have thought only possible with a graphic equaliser and esp, provided I have the correct crystals properly aligned on the shelf next to the record player. Or just buy a Linn cartridge!

Actually, maybe you guys could help me. We are about to go on holiday in our air-conditioned twin axle luxury caravan, which was the ultimate luxury at our local dealers, but what I really wanted was Arthur Weasleys tent and Hermione Grangers bag to carry it in. Can't find them for love nor money down here, but that may be because they are only stocked by Linn dealers.

[Clive197]

Oops! Touchy
My designer kettle lead is actually connected to my designer kettle, which when it lets off steam sounds totally stunning. I have tried other leads but I can't get the same level of infusion.
And while we are about it, what's wrong with a few beers in this sultry weather. If Jack won't come out to play, it makes him a dull boy indeed.

[Oldpinkman]

Oops! Touchy
My designer kettle lead is actually connected to my designer kettle, which when it lets off steam sounds totally stunning. I have tried other leads but I can't get the same level of infusion.
And while we are about it, what's wrong with a few beers in this sultry weather. If Jack won't come out to play, it makes him a dull boy indeed.

Ok - good response. Sorry. Really I should have focussed on debits and credits instead of AOS or playing with HiFi for that matter. Have had the beer you recommended, and will investigate another very shortly. I was in a bad mood because I had to return the Integral and the FX3 today. And bloody Arthur has left me to set up my own PT again (although lots of good news to come). And this thread was causing me grief. I had originally posted that I would like anyone who knew the answer, either from having the HFC article, or because they had the mathematical and engineering skills to calculate an answer, to PM me and not post - since it was primarily intended to spread awe and wonder amongst those like me without engineering skills, rather than test those with them. But it seemed churlish to point that out, and then I found myself sucked into doing hard sums which are not in my normal field, and was busy, and well - its hot too. Good call on the beer.

By the way - if you do know where I can pick up an Arthur Weasley tent that would be handy, because the teenagers are now coming with us for the first week. More beer needed