Math Problem Statement

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Solution

The text in your image is in Indonesian and discusses creating a wave at a specific time and calculating modulation based on given frequency and amplitude values. Here is a breakdown of the information and what we need to calculate:

  1. Given Data for Experiment 1:

    • Frequency of message signal FpF_p = 5 Hz
    • Amplitude of message signal ApA_p = 5
    • Frequency of carrier signal FcF_c = 50 Hz
    • Amplitude of carrier signal AcA_c = 10
  2. Given Data for Experiment 2:

    • Frequency of message signal FpF_p = 5 Hz
    • Amplitude of message signal ApA_p = 5
    • Frequency of carrier signal FcF_c = 50 Hz
    • Amplitude of carrier signal AcA_c = 10

Both sets of data seem identical in values for FpF_p, ApA_p, FcF_c, and AcA_c, indicating they might be testing the stability of modulation.

Step-by-Step Calculation Approach

  1. Calculate Modulation Index (m): The modulation index mm is given by: m=ApAcm = \frac{A_p}{A_c} Substitute the given values: m=510=0.5m = \frac{5}{10} = 0.5

  2. Calculate the Resulting Modulated Frequency:

    • In an amplitude modulation (AM) system, the modulated signal frequency will include the carrier frequency along with sidebands created by adding and subtracting the message frequency.
    • This results in a spectrum with frequencies FcF_c, Fc+FpF_c + F_p, and FcFpF_c - F_p.

    For our values:

    • Carrier frequency Fc=50F_c = 50 Hz
    • Sidebands:
      • Fc+Fp=50+5=55F_c + F_p = 50 + 5 = 55 Hz
      • FcFp=505=45F_c - F_p = 50 - 5 = 45 Hz

Summary of Results

  • Modulation Index mm: 0.5
  • Modulated Frequencies: 50 Hz (Carrier), 55 Hz (Upper Sideband), and 45 Hz (Lower Sideband)

Would you like further details on each calculation step or additional explanations on modulation concepts?


Relative Questions

  1. What is the significance of the modulation index in AM?
  2. How does changing AcA_c or ApA_p affect the modulation index?
  3. Why are sidebands important in amplitude modulation?
  4. How does frequency modulation (FM) differ from amplitude modulation (AM)?
  5. Can the modulation index exceed 1, and if so, what does that imply?

Tip

In AM, the modulation index should ideally stay below 1 to prevent over-modulation, which can lead to signal distortion.

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Math Problem Analysis

Mathematical Concepts

Amplitude Modulation
Frequency Calculation
Modulation Index

Formulas

Modulation Index (m) = Ap / Ac
Upper Sideband Frequency = Fc + Fp
Lower Sideband Frequency = Fc - Fp

Theorems

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Suitable Grade Level

Grades 10-12