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21 March, 23:12

An experimenter finds that standing waves on a string fixed at both ends occur at 24 Hz and 32 Hz, but at no frequencies in between. Part A What is the fundamental frequency

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  1. 21 March, 23:34
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    8 Hz

    Explanation:

    Given that

    Standing wave at one end is 24 Hz

    Standing wave at the other end is 32 Hz.

    Then the frequency of the standing wave mode of a string having a length, l, is usually given as

    f (m) = m (v/2L), where in this case, m could be 1. 2. 3. 4 etc

    Also, another formula is given as

    f (m) = m. f (1), where f (1) is the fundamental frequency ...

    Thus, we could say that

    f (m+1) - f (m) = (m + 1). f (1) - m. f (1) = f (1)

    And as such,

    f (1) = 32 - 24

    f (1) = 8 Hz

    Then, the fundamental frequency needed is 8 Hz
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