LEAVING CERT trigonometry would seem to have little to do with music, but the two are linked.The maths allows iPods and MP3 players to store and play back hours of music using the smallest storage space possible.
This unexpected connection was explained yesterday at a Math’s Week presentation at Waterford Institute of Technology.
Lecturer Michael McCarthy delivered a talk to secondary school students entitled: “How does your iPod work?”
Everyone knows what an iPod does but few know how it does it.
The trick lies in the use of trigonometry to first compress and then to decompress music files so they can be played back again, explained Mr McCarthy, in WIT’s department of engineering technology within electronic engineering. The connection is not immediately apparent, but in fact trigonometry provides the basis of MP3 sound compression.
“If you see trigonometry only as triangles, it would seem odd,” Mr McCarthy said.
The MP3 player uses a set of instructions which tells it how to interpret the sine and cosine shorthand originally used to compress the music file. It is then able to reassemble the original wave file so it can be played back as music, he said.
The compression does eliminate some of the original sounds, but most of these represent sounds that would have been difficult to hear, said Mr McCarthy, who is involved in a flexible wireless and large-scale computing group at WIT.
For example, our ears have difficulty picking out very low frequency signals if there is a competing louder sound playing with it.
The compression system eliminates the unheard low frequency sound in order to make the compressed file that much smaller.
The method works spectacularly well.
Spring, one of the pieces in Antonio Vivaldi’s Four Seasons, would occupy 34 megabytes of space as a wave file but only three megabytes as a file compressed using this trigonometric method, he said. MP3 systems are dependent on this method and without it, services such as digital radio, iTunes and Torrent would not work, he said.
Daily puzzle
IT IS possible to make up 100 using all the digits 1 through 10 (10 may be used as 10 or 1 and 0). You can insert operators (plus, minus, multiply and divide) between them as you wish, but you must use all the digits only once and in that order.
For example, 123 plus 45 minus 67 plus 8 minus 9 times 1 plus 0 equals 100. How many more ways can you find to make 100?
Puzzle answer
The answer to yesterday’s puzzle:
Watson tries a straight cipher: a=1 etc., but this doesn’t yield a clear message. However, Moriarty gives a hint with the word prime and rejecting non-prime numbers yields the clearer message:
3,A,T,3,H,13,5,A,T,13,A,T,H,19,23,5,5,11
CATCH ME AT MATHS WEEK(Prof Moriarty, being a leading 19th century mathematician, defined 1 as non-prime number)