period of a signal is 100 ms. Then the frequency The of this signal in kilohertz is ______.

Question

Prepp Team · Accepted Answer

Understanding Signal Period and Frequency

The question asks us to find the frequency of a signal when its period is given. The period (T) and frequency (f) of a signal are inversely related. This means if you know one, you can easily calculate the other using a simple formula.

Relationship Between Period and Frequency

The fundamental relationship between the period (T) of a signal and its frequency (f) is given by:

$$\text{f} = \frac{1}{\text{T}}$$

Here, T is the time taken for one complete cycle of the signal, and f is the number of cycles the signal completes in one second.

Calculating Signal Frequency in Kilohertz

We are given the period of the signal as 100 milliseconds (ms). To use the formula $f = \frac{1}{T}$, the period must be in seconds (s). We also need the final frequency in kilohertz (kHz).

Let's perform the calculation step-by-step:

Convert Period from Milliseconds to Seconds:
The given period is $T = 100 \text{ ms}$.

We know that $1 \text{ second (s)} = 1000 \text{ milliseconds (ms)}$.

So, $1 \text{ ms} = \frac{1}{1000} \text{ s} = 10^{-3} \text{ s}$.

Therefore, $T = 100 \text{ ms} = 100 \times 10^{-3} \text{ s} = 0.1 \text{ s}$.
Calculate Frequency in Hertz:
Now that the period is in seconds, we can calculate the frequency in Hertz (Hz) using the formula $f = \frac{1}{T}$.

$$f = \frac{1}{0.1 \text{ s}} = \frac{1}{\frac{1}{10} \text{ s}} = 10 \text{ Hz}$$

So, the frequency of the signal is 10 Hz.
Convert Frequency from Hertz to Kilohertz:
The question asks for the frequency in kilohertz (kHz).

We know that $1 \text{ kilohertz (kHz)} = 1000 \text{ Hertz (Hz)}$.

So, $1 \text{ Hz} = \frac{1}{1000} \text{ kHz} = 10^{-3} \text{ kHz}$.

To convert 10 Hz to kHz, we multiply by $10^{-3}$:

$$f = 10 \text{ Hz} = 10 \times 10^{-3} \text{ kHz} = 10^{-2} \text{ kHz}$$

The frequency of the signal is $10^{-2}$ kHz.

Summary of Unit Conversions

Quantity	Unit Conversion
Period (Time)	$1 \text{ ms} = 10^{-3} \text{ s}$
Frequency	$1 \text{ Hz} = 10^{-3} \text{ kHz}$

Let's quickly verify the calculation steps one more time:

Given period $T = 100 \text{ ms}$.
Convert to seconds: $T = 100 \times 10^{-3} \text{ s} = 0.1 \text{ s}$.
Calculate frequency in Hz: $f = \frac{1}{0.1 \text{ s}} = 10 \text{ Hz}$.
Convert to kilohertz: $f = 10 \times 10^{-3} \text{ kHz} = 10^{-2} \text{ kHz}$.

The final result, $10^{-2}$ kHz, matches one of the given options.

Revision Table: Signal Frequency Calculation

Concept	Formula	Key Conversion
Period & Frequency	$f = \frac{1}{T}$	Units must be consistent (e.g., seconds for T, Hertz for f)
Milliseconds to Seconds	$1 \text{ ms} = 10^{-3} \text{ s}$	Divide milliseconds by 1000 to get seconds
Hertz to Kilohertz	$1 \text{ Hz} = 10^{-3} \text{ kHz}$	Divide Hertz by 1000 to get kilohertz

Additional Information: Understanding Signal Characteristics

Understanding signal characteristics like period and frequency is fundamental in many areas of physics and engineering, especially in fields like electronics, telecommunications, and signal processing.

Period (T): Represents the duration of one complete cycle of a repeating waveform. It is measured in units of time, such as seconds (s), milliseconds (ms), microseconds ($\mu$s), etc.
Frequency (f): Represents the number of cycles of a repeating waveform that occur in one second. It is measured in Hertz (Hz), which is equivalent to cycles per second. Other common units include kilohertz (kHz), megahertz (MHz), and gigahertz (GHz).

The inverse relationship $f = \frac{1}{T}$ highlights that a shorter period means a higher frequency (more cycles per second), and a longer period means a lower frequency (fewer cycles per second).