Beatles Forever
The needle on a grammophone travels from the edge of the record towards the center when a LP record is played. If there are 630 tracks with the closest 6 cm from the center and the one furthest 15 cm away, how many cm does the needle travel?
December 11th, 2008 at 5:11 am
9cm. Last time I looked at a phonograph (my gramophone is in the shop), the needle was mounted on an arm that only moved radially towards the center of the disk, and the record did all the long distance moving.
And…there’s only ONE groove per side.
December 11th, 2008 at 7:50 am
There’s at least one Monty Python record with 2 grooves on one side, and apparently a few others as well:
http://www.snopes.com/music/media/groove.asp
Imagine playing a record a few times, and then the next time you play it, something totally different comes out! It wasn’t advertised that the record was like this, so it was quite surprising!
December 12th, 2008 at 3:15 am
2 grooves? How cool! I want one!
December 12th, 2008 at 4:49 am
Groovy.
December 17th, 2008 at 2:59 am
Sure, this may be a trick question, but the needle does move with respect to the surface of the record, and it moves a lot more than 9 cm. The total distance traveled is probably a good measure of when to replace the needle, so it is worthwhile to calculate this distance.
There may be only one groove, but if I place a string along a radius of the record, it passes over a whole lot of ridges. We are given that at the innermost ridge (n=1), the radius is 6 cm, and at t the outermost ridge (n=630) the radius is 15 cm. So I could write r = f(n) = (9/629)(n-1) + 6, and an approximation for the length the needle travels is 2*pi*Sum(f(n),1,630). I get 13230*pi or about 416 meters.
A moment with Google will turn up the exact formula. This approximation is quite good.
Years ago I had one of those multi-groove records. It came inside an issue of Mad Magazine.
May 15th, 2010 at 3:35 am
My mom wants me to cut my hair like Beatles – I hate it