An audio signal of amplitude one half the carrier amplitude is used in an amplitude modulation. The modulation index is

Options

A. 2
B. 0.25
C. 0.5
D. 0.125

Answer

To find the modulation index for the given audio signal in amplitude modulation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Modulation Index Formula**:
The modulation index (μ) in amplitude modulation is defined as:
\[ \mu = \frac{A_m}{A_c} \]
where \(A_m\) is the amplitude of the modulating signal (audio signal) and \(A_c\) is the amplitude of the carrier wave.

2. **Identify the Given Information**:
According to the problem, the amplitude of the audio signal is one half of the carrier amplitude. This can be expressed as:
\[ A_m = \frac{1}{2} A_c \]

3. **Substitute the Value of \(A_m\) in the Modulation Index Formula**:
We can substitute \(A_m\) in the modulation index formula:
\[ \mu = \frac{A_m}{A_c} = \frac{\frac{1}{2} A_c}{A_c} \]

4. **Simplify the Expression**:
When we simplify the expression, we notice that \(A_c\) in the numerator and denominator cancels out:
\[ \mu = \frac{1}{2} \]

5. **Final Result**:
Therefore, the modulation index is:
\[ \mu = 0.5 \]

### Conclusion:
The modulation index for the given audio signal is **0.5**.

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