Question

Which of these frequencies is resonant with that of an ideal `"256 Hz"` tuning fork?

`"512 Hz"`, `"400 Hz"`, `"441 Hz"`, `"300 Hz"`

Answer 1

Resonant frequencies are frequencies that coincide with the natural emitted frequency. I would have actually said `"512 Hz"`, as the first harmonic in a tuning fork relative to a `"256 Hz"` fundamental has a frequency of `"512 Hz"`.

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Most pure waveforms (square, saw, triangle, etc), except sine waves, are a linear combination of the fundamental, and the `n`th harmonics, `n = 1, 2, 3, . . .`.

Thus, each successive harmonic is quieter than the previous, but all of them are present to some extent.

The `n`th harmonic in `"Hz"` is found as

`f_"fund" xx 2^n`

where `f_"fund"` is the fundamental frequency.

So, for example, a sine wave plays `f_"fund" = "261.6 Hz"` on middle C. The 1st harmonic is thus at

`"261.6 Hz" xx 2^1 = "523.2 Hz"`

and so on by doubling the frequency of each successive harmonic.

So, the tuning fork would be primarily composed of a slightly flat middle C, and smaller contributions from higher octaves. But if one could filter out the fundamental, e.g. with a band notch filter, a frequency of `"512 Hz"` would resonate with a slightly flat C an octave above middle C.