Answer: Calculate the period by dividing the reciprocal of frequency, and frequency by dividing the reciprocal of period.

Explanation:

The period of a wave is defined as the time it takes for one complete cycle of the wave to occur. It is typically denoted by the symbol T. On the other hand, frequency represents the number of cycles of the wave that occur in one unit of time, often measured in hertz (Hz), where 1 Hz equals one cycle per second.

Here’s a detailed explanation of how to calculate the period and frequency:

1. Period Calculation:
   • To calculate the period T of a wave, you can use the formula: [Tex] [ T = \frac{1}{f} ] [/Tex]
   • This formula arises from the fact that frequency and period are inversely related: as frequency increases, the period decreases, and vice versa. Thus, taking the reciprocal of the frequency gives us the period.
2. Frequency Calculation:
   • Conversely, to calculate the frequency f of a wave, you can use the formula: [Tex][ f = \frac{1}{T} ][/Tex]
   • This formula follows from the definition of frequency as the reciprocal of the period: frequency represents how many cycles occur per unit time, so the inverse of the period gives us the frequency.
3. Units:
   • Period is typically measured in units of time, such as seconds (s).
   • Frequency is measured in hertz (Hz), where 1 Hz equals one cycle per second.
4. Example:
   • Suppose you have a wave with a period of T=0.02 seconds. To find the frequency, you would use the formula [Tex][ f = \frac{1}{T} = \frac{1}{0.02} = 50 \, \text{Hz} ][/Tex]
   • This means that the wave completes 50 cycles every second.

In summary, the period of a wave represents the time it takes for one complete cycle, and the frequency represents the number of cycles that occur in one unit of time. You can calculate the period by taking the reciprocal of the frequency, and the frequency by taking the reciprocal of the period. These calculations allow you to relate the time domain (period) to the frequency domain (frequency) of a wave, providing insights into its behavior and characteristics.