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Math Help - trig formula for oscillations per second

  1. #1
    Senior Member furor celtica's Avatar
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    trig formula for oscillations per second

    A tuning fork is vibrating. The displacement, y centimetres, of the tip of one of the prongs from its rest position after t seconds is given by
    y= 0.1sin(100 000t)
    Find :
    a. the greatest displacement and the time at which it first occurs,
    b. the time taken for one complete oscillation of the prong,
    c. the number of complete oscillations per second of the tip of the prong

    I answered a. and b. correctly with the following responses:
    a. y= 0.1 cm., t= 0.000 9 s.
    b. 0.003 6 s.

    For c. I answered 277 (complete oscillation p/s) taking the answer to b.
    1/0.0036 = 277.8 (correct to 1 d.p.)
    Which makes 277 complete oscillations per second.

    However the correct answer is given to be 278.
    Why is this?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: trig formula for oscillations per second

    I think 277,8 is approximately 278.
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  3. #3
    Senior Member furor celtica's Avatar
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    Re: trig formula for oscillations per second

    complete oscillations per second
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  4. #4
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    mr fantastic's Avatar
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    Re: trig formula for oscillations per second

    Quote Originally Posted by furor celtica View Post
    complete oscillations per second
    Assuming 277.8 is correct, then your answer is correct and the book is wrong. A classic case of where rounding for context overrides the mathematical rules for rounding.
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