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Chapter 2: Problem 3

A square wave has a frequency of \(25 \mathrm{~Hz}\). What is its period?

Short Answer

Expert verified
The period of the 25 Hz square wave is 0.04 seconds.

Step by step solution

01

Understand the Relationship Between Frequency and Period

The period, T, of a wave is the inverse of its frequency, f, given by the formula T = 1/f. The frequency is the number of cycles per second, and the period is the time it takes for one complete cycle of the waveform.
02

Insert the Given Frequency into the Formula

Given that the frequency f is 25 Hz, you can find the period T by substituting the frequency into the formula: T = 1/f = 1/25.
03

Calculate the Period

Carry out the division to find the period: T = 1/25 = 0.04 seconds. Therefore, the period of the square wave is 0.04 seconds.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Waveform Analysis
Waveform analysis allows us to examine the shape of a wave and derive meaningful insights about its behavior. This can include looking at a wave鈥檚 amplitude, frequency, phase, and period. Each of these attributes defines certain characteristics of the wave. For example, the frequency of a wave tells us how many times a particular pattern occurs within a second, which is measured in Hertz (Hz). In our case, analyzing a square wave with a frequency of 25 Hz means that the pattern repeats 25 times each second. By understanding waveform analysis, students are better equipped to manipulate and predict how waveforms will interact with different systems.
Characteristics of a Square Wave
A square wave is a non-sinusoidal periodic waveform that switches between a high and a low state at regular intervals. It is characterized by its sharp transitions, or 'flips,' from one state to the other. Square waves have a duty cycle of 50%, which means that the wave is at its high state for half of the period and low for the other half. This waveform is commonly used in digital electronics and signal processing because of its simplicity and ease of triggering circuits. It鈥檚 important to note that a square wave contains a fundamental frequency along with odd harmonics, which can have implications in various applications.
Inverse Relationship Between Frequency and Period
The concept of an inverse relationship is critical when studying waves. It means that as one quantity increases, the other decreases. In the context of waves, frequency and period share this type of relationship, as showcased by the formula for period (\( T = \frac{1}{f} \) ). If the frequency of a wave increases, its period shortens, meaning it takes less time for one full cycle to occur. Conversely, a lower frequency means a longer period, indicating a slower oscillation. Understanding this inverse correlation helps in predicting how a wave behaves over time, which is essential in fields like telecommunications, sound engineering, and physics as a whole.

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