One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a

Question

One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column?

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Ngọc Hoa 4 years 2021-08-31T09:24:05+00:00 1 Answers 16 views 0

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  1. Maris
    0
    2021-08-31T09:26:03+00:00
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    Answer:

    Fundamental frequency of the air column is 128 Hz

    Explanation:

    The general relation to determine the nth- harmonic in column of air is:

    f_{n} =nf_{1}

    Here n is nth harmonic and f₁ is the fundamental frequency of the air column.

    According to the problem, there are two consecutive harmonics, one of the order n and other is n+1. Thus, there frequencies are given by :

    f_{n} =nf_{1}       …..(1)

    f_{n+1} =(n+1)f_{1}      ….(2)

    Subtract equation (2) and (1).

    f_{n+1}-f_{n} =f_{1}

    Substitute 576 Hz for f_{n+1} and 448 Hz for f_{n} in the above equation.

    (576 – 448 ) Hz = f₁

    f₁ = 128 Hz

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