If the period of an oscillator doubles, what happens to its frequency?
f = 1/T
f/2 = 1/(2T)
To understand what happens to the frequency of an oscillator when its period doubles, we first need to understand the relationship between period and frequency.
The period of an oscillator is the time it takes for one complete cycle of oscillation. It is commonly measured in seconds (s).
The frequency of an oscillator, on the other hand, is the number of cycles or oscillations it completes in a given time period. It is usually measured in Hertz (Hz), which represents the number of cycles per second.
So, the relationship between period and frequency can be expressed as:
Frequency = 1 / Period
Now, if the period of an oscillator doubles, it means it takes twice as long to complete one cycle. This can be mathematically represented as:
New Period = 2 * Old Period
Using the relationship between period and frequency, we can determine the effect on frequency:
New Frequency = 1 / New Period
= 1 / (2 * Old Period)
= (1/2) * (1 / Old Period)
= (1/2) * Old Frequency
Therefore, if the period of an oscillator doubles, its frequency will be halved. In other words, the frequency is reduced by a factor of 2.