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24 December, 12:57

A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 450 Hz. The next higher harmonic has a frequency of 750 Hz. The speed of sound in air is 343 m/s.

(a) What is the integer n that describes the harmonic whose frequency is 450 Hz?

(b) What is the length of the tube?

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  1. 24 December, 14:49
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    Answer: the correct answer is a) the interger is n = 3

    b) the length of the tube L = 0.57 m

    Explanation:

    For a tube that is open at one end, nth harmonic frequency is given by

    fn=n (v/4L)

    the next higher harmonic frequency is given by

    fn+2=n+2 (v/4L)

    Now we have the ratio

    fn+2/fn = (n+2) / n = 1+2/n

    2/n = [ (fn+2) / fn]-1 or

    n = 2/{[ (fn+2) / fn]-1}

    (a) In the problem we have

    fn = 450Hz and fn+2 = 750Hz So,

    n=2/[ (750/450) - 1] = 3

    then the frequency of 450Hz corresponds to n=3

    b) then we have

    450=3v/4L so, L = 3v / (4*450) (3*343) / (4*450) = 0.57m
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