The period and frequency of a wave are inversely related.
To understand why the period and frequency of a wave are inversely related, we need to define what both terms represent.
The period of a wave is the time it takes for one complete wave cycle to pass a given point. It is usually denoted by the symbol "T" and is measured in seconds.
The frequency of a wave, on the other hand, is the number of complete wave cycles that pass a given point in one second. It is usually denoted by the symbol "f" and is measured in hertz (Hz).
Now, let's consider the relationship between the period and frequency of a wave. The key to understanding their inverse relationship lies in the definition of frequency: the number of wave cycles per second. Since frequency is a measure of how frequently wave cycles occur, it is natural to think that when the frequency is higher, the waves are occurring more frequently.
Mathematically, the relationship between period and frequency can be expressed using the formula:
frequency (f) = 1 / period (T)
This equation tells us that the frequency is equal to the reciprocal of the period. In other words, if the period of a wave becomes smaller (i.e., it takes less time for one complete cycle), the frequency increases because more wave cycles are occurring in a given second. Conversely, if the period becomes larger (i.e., it takes more time for one complete cycle), the frequency decreases because fewer wave cycles are occurring in a given second.
To summarize, the period and frequency of a wave are inversely related: as the period increases, the frequency decreases, and vice versa. This relationship is described by the equation f = 1/T, where f is the frequency and T is the period.