Determine the frequency of the 2nd harmonic of a spring that has a 3rd harmonic resonance of f3=512 Hz. a.341 Hz

Question

Determine the frequency of the 2nd harmonic of a spring that has a 3rd harmonic resonance of f3=512 Hz.

a.341 Hz

b.768 Hz

c.1536 Hz

d.512 Hz

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Tryphena 2 weeks 2021-07-22T07:39:49+00:00 1 Answers 4 views 0

Answers ( )

    0
    2021-07-22T07:40:57+00:00

    Answer:

    1) 341 Hz

    Explanation:

    When a string vibrates, it can vibrate with different frequencies, corresponding to different modes of oscillations.

    The fundamental frequency is the lowest possible frequency at which the string can vibrate: this occurs when the string oscillate in one segment only.

    If the string oscillates in n segments, we say that it is the n-th mode of vibration, or n-th harmonic.

    The frequency of the n-th harmonic is given by

    f_n = nf_1

    where

    n is the number of the harmonic

    f_1 is the fundamental frequency

    Here we have:

    f_3=512 Hz is the frequency of the 3rd harmonic

    So the fundamental frequency is

    f_1=\frac{f_3}{3}=\frac{512}{3}=170.7 Hz

    And so, the frequency of the 2nd harmonic is:

    f_2=2f_1=2(170.7)=341.3 Hz

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