What equation describes the relationship between frequency and period?

The relationship between frequency and period is foundational in understanding wave phenomena and oscillations. Frequency, measured in Hertz (Hz), indicates the number of cycles a wave completes in one second. The period, measured in seconds, is the duration it takes to complete one full cycle.

The correct equation articulates that frequency is the reciprocal of the period. This means that for any wave or oscillation, if you know the period (how long it takes to complete one cycle), you can easily find the frequency by taking the inverse. The formula states that frequency (in Hz) equals one divided by the period (in seconds). Thus, if the period increases, the frequency decreases, and vice versa. This direct reciprocal relationship is fundamental in both theoretical and practical applications of vibration analysis and signal processing.

For example, if a machine vibrates with a period of 2 seconds, its frequency would be 1/2 = 0.5 Hz, indicating it completes half a cycle per second. Recognizing this relationship helps in analyzing vibration data and understanding how changes in vibrational characteristics can affect system behavior.

The other options present inaccurate interpretations of the frequency-period relationship, either by suggesting they are equivalent or incorrectly linking them through incorrect mathematical operations.