Question
Explain how the frequency of a wave changes when the period of the wave increases
Answers
GPT-4o mini
The frequency of a wave is inversely related to its period. The frequency (\(f\)) is defined as the number of cycles (or waves) that pass a given point per unit of time, usually expressed in hertz (Hz), which is equivalent to cycles per second. The period (\(T\)) is the time it takes for one complete cycle of the wave to pass a given point, expressed in seconds.
The relationship between frequency and period can be described by the equation:
\[
f = \frac{1}{T}
\]
From this equation, we can see that if the period \(T\) increases (meaning it takes longer for one complete cycle to occur), the frequency \(f\) decreases. This is because a longer period means fewer cycles occur in a given time frame.
For example, if the period of a wave increases from 1 second to 2 seconds, the frequency would change from 1 Hz (1 cycle per second) to 0.5 Hz (0.5 cycles per second). Thus, as the period increases, the frequency decreases, demonstrating their inverse relationship.
The relationship between frequency and period can be described by the equation:
\[
f = \frac{1}{T}
\]
From this equation, we can see that if the period \(T\) increases (meaning it takes longer for one complete cycle to occur), the frequency \(f\) decreases. This is because a longer period means fewer cycles occur in a given time frame.
For example, if the period of a wave increases from 1 second to 2 seconds, the frequency would change from 1 Hz (1 cycle per second) to 0.5 Hz (0.5 cycles per second). Thus, as the period increases, the frequency decreases, demonstrating their inverse relationship.