The amplitude of the modulating wave is `2//5` th of the amplitude of the carrier wave. The percentage modulation

Options

A. 20
B. 40
C. 50
D. 60

Answer

To solve the problem, we need to find the percentage modulation given that the amplitude of the modulating wave is \( \frac{2}{5} \) of the amplitude of the carrier wave. Here’s a step-by-step solution:

### Step 1: Understand the relationship between amplitudes
Let:
- \( A_c \) = Amplitude of the carrier wave
- \( A_m \) = Amplitude of the modulating wave

According to the problem, the relationship between the amplitudes is given by:
\[ A_m = \frac{2}{5} A_c \]

### Step 2: Calculate the modulation index
The modulation index \( m \) is defined as the ratio of the amplitude of the modulating wave to the amplitude of the carrier wave:
\[ m = \frac{A_m}{A_c} \]
Substituting the values we have:
\[ m = \frac{2/5 A_c}{A_c} = \frac{2}{5} \]

### Step 3: Convert modulation index to percentage modulation
Percentage modulation is calculated using the formula:
\[ \text{Percentage Modulation} = m \times 100 \]
Substituting the value of \( m \):
\[ \text{Percentage Modulation} = \frac{2}{5} \times 100 \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ \text{Percentage Modulation} = 0.4 \times 100 = 40\% \]

### Final Answer
The percentage modulation is \( 40\% \).

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