To find the frequency of a wave when you know its period, you use the inverse relationship between the two properties. The frequency is simply the reciprocal of the period.
Understanding Frequency and Period
- Frequency (f): The number of cycles or oscillations a wave completes in one second. It is typically measured in Hertz (Hz), where 1 Hz equals one cycle per second.
- Period (T): The time it takes for a wave to complete one full cycle or oscillation. It is typically measured in seconds (s).
Think of them as two sides of the same coin: frequency tells you how many cycles happen in a second, while period tells you how long one cycle takes.
The Formula
The fundamental relationship between frequency (f) and period (T) is defined by the following formula:
f = 1 / T
This means that frequency is equal to 1 divided by the period. Conversely, the period is equal to 1 divided by the frequency (T = 1 / f).
As mentioned in the reference, the relationship between the period (T) and frequency (f) is such that T = 1 f (standardly written as T = 1/f), indicating their inverse proportionality. Once the period (T) is known, finding the frequency (f) is a straightforward calculation using this inverse relationship.
How to Calculate Frequency from Period
To calculate the frequency from the period, follow these simple steps:
- Identify the known value: the period (T) of the wave. Ensure the period is in seconds.
- Use the formula f = 1 / T.
- Divide 1 by the value of the period (T).
- The result will be the frequency (f) in Hertz (Hz).
Example Calculation
Let's say you have a wave with a period of 0.5 seconds.
- Known: Period (T) = 0.5 s
- Formula: f = 1 / T
- Calculation: f = 1 / 0.5 s = 2 Hz
So, the frequency of the wave is 2 Hertz. This means the wave completes 2 cycles every second.
Here's another example:
| Period (T) | Calculation (f = 1/T) | Frequency (f) |
|---|---|---|
| 1 second | f = 1 / 1 | 1 Hz |
| 0.1 seconds | f = 1 / 0.1 | 10 Hz |
| 2 seconds | f = 1 / 2 | 0.5 Hz |
Knowing the period makes finding the frequency very easy using this simple reciprocal relationship.
