If a wave’s third harmonic has a frequency of 24 Hz, what is its natural (fundamental) frequency and what is the frequency of H6?

Question

If a wave’s third harmonic has a frequency of 24 Hz, what is its
natural (fundamental) frequency and what is the frequency of H6?

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Minh Khuê 2 months 2021-08-01T22:50:37+00:00 1 Answers 2 views 0

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    0
    2021-08-01T22:52:18+00:00

    Answer:

    8 Hz, 48 Hz

    Explanation:

    The standing waves on a string (or inside a pipe, for instance) have different modes of vibrations, depending on how many segments of the string are vibrating.

    The fundamental frequency of a standing wave is the frequency of the fundamental mode of vibration; then, the higher modes of vibration are called harmonics. The frequency of the n-th harmonic is given by

    f_n = nf_1

    where

    f_1 is the fundamental frequency

    In this problem, we know that the wave’s third harmonic has a frequency of

    f_3=24 Hz

    This means this is the frequency for n = 3. Therefore, we can find the fundamental frequency as:

    f_1=\frac{f_3}{3}=\frac{24}{3}=8 Hz

    Now we can also find the frequency of the 6-th harmonic using n = 6:

    f_6 = 6 f_1 = 6 (8)=48 Hz

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