In an amplitude modulation with modulation index 0.5 the ratio of the carrier wave to that of side band in the modulated wave is

Options

A. `4:1`
B. `1:4`
C. `1:3`
D. `2:1`

Explanation

To solve the problem of finding the ratio of the carrier wave to that of the sideband in an amplitude modulation with a modulation index of 0.5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Modulation Index**:
The modulation index (µ) in amplitude modulation is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave. In this case, µ = 0.5.

2. **Identify the Amplitude of the Carrier Wave**:
Let the amplitude of the carrier wave be denoted as \( A_C \).

3. **Calculate the Amplitude of the Sideband**:
The amplitude of the sideband can be expressed in terms of the modulation index and the amplitude of the carrier wave. The formula is:
\[ A_{SB} = \frac{\mu A_C}{2} \]
Substituting the given value of µ:
\[ A_{SB} = \frac{0.5 A_C}{2} = \frac{0.5}{2} A_C = 0.25 A_C \]

4. **Determine the Ratio of Carrier to Sideband**:
We need to find the ratio of the amplitude of the carrier wave to the amplitude of the sideband:
\[ \text{Ratio} = \frac{A_C}{A_{SB}} = \frac{A_C}{0.25 A_C} \]
Simplifying this gives:
\[ \text{Ratio} = \frac{1}{0.25} = 4 \]

5. **Express the Ratio in Standard Form**:
The ratio can be expressed as:
\[ \text{Ratio} = 4:1 \]

### Final Answer:
The ratio of the carrier wave to that of the sideband in the modulated wave is \( 4:1 \).

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