What is the relationship between frequency and period?

The relationship between frequency and period is that the period is the reciprocal of frequency. This means that if you know the frequency (the number of cycles per second) of a wave, you can find the period (the time taken for one complete cycle) by taking the inverse of the frequency. Mathematically, this relationship is expressed as:

[ \text{Period} (T) = \frac{1}{\text{Frequency} (f)} ]

or conversely,

[ \text{Frequency} (f) = \frac{1}{\text{Period} (T)} ]

This indicates that as frequency increases, the period decreases, and vice versa. Understanding this relationship is fundamental in wave mechanics, as it helps in calculating various properties of waves when certain parameters are known.

Other options misrepresent the conceptual relationship. For instance, stating that the period is always double the frequency does not hold in the physics of waves. Similarly, suggesting that period and frequency are independent contradicts their inherent connection, and the notion of frequency being the square of the period also does not align with the correct mathematical relationship.