Question

Suppose the amplitude of modulated wave equal to the signal amplitude. Then modulation is (A) \(10 \%\) (B) \(25 \%\) (C) \(50 \%\) (D) \(100 \%\)

Short answer

Since we don't have enough information to calculate the modulation percentage, we cannot choose the correct option from the given choices. However, the modulation index (m) can be found by the formula \(m = \frac{A_m}{A_c}\), where \(A_m\) is the amplitude of the modulated wave and \(A_c\) is the amplitude of the carrier wave. To express the modulation index as a percentage, multiply it by 100.

Step-by-step solution

Write down the given information

We are given that the amplitude of the modulated wave (\(A_m\)) is equal to the signal amplitude (\(A_s\)). That is, \(A_s = A_m\).

Calculate the modulation index (m)

Recall that the modulation index (m) can be calculated using the formula: \[m = \frac{A_s}{A_c}\] From the given information, we know that \(A_m = A_s\). Thus, the modulation index becomes: \[m = \frac{A_m}{A_c}\]

Express modulation index in percentage

To express the modulation index (m) in percentage, we need to multiply it by 100. Therefore, Modulation percentage = \(m × 100\)

Compare the calculated modulation percentage with the given options

As we have found the formula for modulation percentage, we will now compare it with the given options. (A) \(10 \%\) (B) \(25 \%\) (C) \(50 \%\) (D) \(100 \%\) Since we don't have enough information to determine the exact modulation percentage, we can't select one of the provided options. However, this exercise acts as a guide on how to calculate the modulation percentage given the amplitude of the modulated wave and carrier wave.