Given the following periods in milliseconds (ms), convert the period to seconds (s) and calculate the frequency (Hz). 0.125 ms 0.250 ms 0.500 ms 1.000 ms 2.000 ms 500.00 ms 1000.00 ms
The Correct Answer and Explanation is:
To solve this problem, two conversions are necessary:
- Milliseconds (ms) to seconds (s):
Since 1 second = 1000 milliseconds, divide the given value by 1000. - Period to frequency:
Frequency (Hz) is the reciprocal of the period in seconds.
Formula:
f=1Tf = \frac{1}{T}f=T1
Where f is frequency in hertz (Hz), and T is the period in seconds (s).
Conversions and Calculations
| Period (ms) | Period (s) | Frequency (Hz) |
|---|---|---|
| 0.125 ms | 0.000125 s | 8000 Hz |
| 0.250 ms | 0.000250 s | 4000 Hz |
| 0.500 ms | 0.000500 s | 2000 Hz |
| 1.000 ms | 0.001000 s | 1000 Hz |
| 2.000 ms | 0.002000 s | 500 Hz |
| 500.00 ms | 0.500000 s | 2 Hz |
| 1000.00 ms | 1.000000 s | 1 Hz |
Explanation
The period of a wave or signal is defined as the time taken for one complete cycle. It is often given in milliseconds (ms), particularly when dealing with high-frequency signals, such as in electronics or communications. To standardize units for further calculations, the period must be converted to seconds (s). This is achieved by dividing the millisecond value by 1000, since there are 1000 milliseconds in one second.
Once the period is expressed in seconds, the next step involves determining the frequency. Frequency measures how many cycles occur in one second and is expressed in hertz (Hz). Mathematically, frequency is the inverse of the period. For example, if a signal has a period of 0.001 seconds, then the frequency is 1 divided by 0.001, resulting in 1000 Hz. This means the signal completes 1000 cycles per second.
This relationship shows that shorter periods correspond to higher frequencies and vice versa. A period of 0.125 ms (which is 0.000125 s) results in a high frequency of 8000 Hz. On the other hand, a long period such as 1000 ms (or 1 second) corresponds to a low frequency of 1 Hz.
This principle is fundamental in signal processing, telecommunications, and many areas of physics and engineering. Understanding the inverse relationship between period and frequency allows for accurate analysis and design of systems involving waves, such as sound, light, and electronic signals.
