Which of the following frequencies are associated with sub-harmonics?

Sub-harmonics are frequencies that occur at fractions of a fundamental frequency. Specifically, half-integer frequencies refer to those that are represented as a fraction of the fundamental frequency, such as 1/2, 1/3, or similar values. This means they are lower than the fundamental frequency and typically correlate with system behavior, where forces cause the system to vibrate at these reduced frequency levels.

In the context of vibration analysis, recognizing sub-harmonics is crucial because they can indicate specific dynamic behaviors or issues such as resonance or instability within mechanical systems. Half-integer frequencies are a clear example of this concept since they are directly representative of sub-harmonic action within the vibrational spectrum.

The other options don’t represent sub-harmonics effectively. The 1x series consists of integer multiples of the fundamental frequency, while integer multiples and random frequencies do not fit the definition of sub-harmonics as they do not indicate a lower-fractal relationship to a fundamental frequency. Understanding this distinction helps in diagnosing and analyzing vibration-related issues in mechanical systems.