Math Problem Statement

What is the period and frequency of the GREEN wave?

What is the period and frequency of the GREEN wave?

Solution

To analyze the green waveform in the provided image and determine its period and frequency, let's first examine the following key points from the graph:

  1. Period: The period TT is the time it takes for the waveform to complete one full cycle.
  2. Frequency: The frequency ff is the reciprocal of the period, given by f=1Tf = \frac{1}{T}.

Step-by-step breakdown:

  • The green waveform appears to have a square shape. From the graph:
    • It starts at time t=0t = 0 seconds with a value of 0 V.
    • The first rise occurs at about t=tat = t_a, which looks like ta=0.1t_a = 0.1 seconds.
    • It remains at a high value (approximately 5 V) until t=tbt = t_b, which appears to be at tb=0.75t_b = 0.75 seconds.
    • The waveform then drops back to 0 V and completes its cycle after repeating this pattern.

Period Calculation:

The period TT is the time between successive repeats of the pattern. Based on the graph:

  • One cycle starts at t=0t = 0 s and repeats after t=1.5t = 1.5 s.

Thus, the period of the green waveform is: T=1.5secondsT = 1.5 \, \text{seconds}

Frequency Calculation:

The frequency is the reciprocal of the period: f=1T=11.5=0.67Hzf = \frac{1}{T} = \frac{1}{1.5} = 0.67 \, \text{Hz}

Summary:

  • Period of the green waveform: 1.5 seconds
  • Frequency of the green waveform: 0.67 Hz

Would you like more details on any part of this analysis?

Here are 5 relative questions to expand this discussion:

  1. How does the period of a waveform affect its frequency?
  2. What is the relationship between the green waveform and the blue waveform?
  3. How can we calculate the duty cycle for a square wave?
  4. Can we determine the voltage levels of the green wave more precisely from this graph?
  5. How can we extract the time constants of the blue waveform?

Tip: For periodic waveforms like square waves, the duty cycle (time spent high versus the total period) is often an important characteristic to evaluate the signal's behavior.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Waveform Analysis
Period and Frequency

Formulas

Period T = time to complete one cycle
Frequency f = 1/T

Theorems

Basic periodic waveform analysis in signal processing

Suitable Grade Level

Undergraduate (Electrical Engineering, Signal Processing)