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For $N$ equally spaced samples at sampling rate $f_s$, the discrete Fourier transform has frequency bins spaced by $f_s/N=1/T_{\mathrm{obs}}$. A rectangular observation window broadens a sinusoid into a sinc function profile whose nearest zeros are $1/T_{\mathrm{obs}}$ from its central frequency. This sets a conventional scale for distinguishing nearby spectral components. It is not a universal lower bound on the uncertainty of frequency estimation for an isolated tone: a specified signal model and noise level can allow precision finer than the bin spacing. Padding with zeros interpolates the spectral display without increasing the observation duration.

Frequency estimation infers a periodic signal's frequency from observed samples. It may use a peak of the discrete Fourier transform, or fit a sinusoidal model with amplitude, phase, and frequency as unknown parameters. Its attainable precision depends on noise, observation duration, sampling rate, and the estimator. Fourier frequency resolution alone does not specify that precision.

For the $110\mathrm{Hz}$ fundamental alone, the Nyquist–Shannon sampling theorem places the limiting sampling rate at twice that frequency:Use a rate strictly above this boundary for a sinusoid of unknown phase: exactly two samples per cycle can, for a particular phase, all fall at zero. If higher Fourier harmonics are retained, the sampling rate must instead exceed twice the highest retained frequency, or those components must be removed to prevent aliasing.

For a straightforward discrete Fourier transform estimate, Fourier frequency resolution obeys $\Delta f\sim 1/T_{\mathrm{obs}}$. Resolving $0.07\mathrm{Hz}$ therefore suggestsAt the limiting sampling rate this is about $f_s{T}_{\mathrm{obs}}\simeq 3143$ samples. These are the usual sampling and spectral-resolution estimates. The $14.3\mathrm{s}$ value is not a universal lower bound on single-tone frequency estimation: fitting a sinusoidal model with sufficiently low noise can estimate its frequency more precisely than the spacing of discrete Fourier transform bins. The question gives no noise level or estimator, so a sharper universal minimum time cannot be deduced.