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Harshal Gajjar

  • When is 50 cycles per second not equal to 25 cycles per half second [perspective]

    By harshalgajjar

    On 2017-01-15 00:18:21

    I've started a new section called Perspective on my blog in which I will be posting answers to random questions to which answers I thought obvious were false... Here goes my first post in this section:

    Till day before yesterday I used to think that something happening 50 times a second would happen 25 times every half second. This was pretty obvious to not only me but also several of my friends, but it turns out this isn't necessarily true.

    Let's suppose I have a bell which rings 10 times in the first second, doesn't ring in the second second (haha), then rings 10 times in the third, then again doesn't ring in the next, this goes on... (till? comment below)

    So, basically this bell shows a 2 second cyclicity, i.e. 1 cycle every two second.But because the bell rings only in the second half of the cycle, I can't really say that it completes half cycle every two second.

    Let's explore the reason a bit more:
    If my friend Parth is a sound editor and I happen to recreate the sound of the bell I have. I go to him and tell him that my bell rings 10 times every 2 seconds (which is correct) and walk back home.
    Next day he calls me and I visit his store again. But I realise that the track doesn't sound like the bell. The track "rang" 5 times every second, i.e. half a cycle every second.

    By now it probably is clear that 10 cycles* every 2 seconds is NOT always equal to 5 cycles* every 1 second.

    This though made me do a bit of research, on 2 units - hertz and becquerel, which ended when I read the following:

    The rate at which aperiodic or stochastic events occur may be expressed in becquerels (as in the case of radioactive decay), not hertz, since although the two are mathematically similar by convention hertz implies regularity where becquerels implies the requirement of a time averaging operation. Thus, 1 Bq is 1 event per second on average whereas 1 hertz is 1 event per second on a regular cycle.

    See you in the comments. :)

    *Oxford Dictionary, Merriam Webster, and don't mention that the cycles must be evenly distributed with respect to time

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