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  • Resonant Frequencies of a Vibrating String: Understanding Harmonics
    A vibrating string will be resonant at its fundamental frequency and all of its harmonics. Here's how it works:

    * Fundamental Frequency: This is the lowest frequency at which the string can vibrate, which you've given as 30 Hz.

    * Harmonics: These are multiples of the fundamental frequency.

    So, the vibrating string will also be resonant at:

    * 2nd harmonic: 30 Hz * 2 = 60 Hz

    * 3rd harmonic: 30 Hz * 3 = 90 Hz

    * 4th harmonic: 30 Hz * 4 = 120 Hz

    * And so on...

    In general, the resonant frequencies of a vibrating string are given by:

    * f = n * f₀ where:

    * f is the resonant frequency

    * n is the harmonic number (1, 2, 3, ...)

    * f₀ is the fundamental frequency

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