An sudio signal `V_(m)=15omega_(1)t` is modulated on a CW of `V_(c)=60 sin omega_(2)t`. The percentage modulation is

Options

A. `50%`
B. `40%`
C. `25%`
D. `2.5%`

Answer

To solve the problem of finding the percentage modulation of the given audio signal modulated on a carrier wave, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Signals**:
- The audio signal is given as \( V_m = 15 \omega_1 t \).
- The carrier wave is given as \( V_c = 60 \sin(\omega_2 t) \).

2. **Determine the Amplitudes**:
- The amplitude of the audio signal \( V_m \) is \( 15 \).
- The amplitude of the carrier wave \( V_c \) is \( 60 \).

3. **Calculate the Modulation Index**:
- The modulation index \( m \) is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier signal:
\[ m = \frac{V_m}{V_c} = \frac{15}{60} \]

4. **Simplify the Modulation Index**:
- Simplifying the fraction:
\[ m = \frac{1}{4} \]

5. **Calculate the Percentage Modulation**:
- The percentage modulation is given by the formula:
\[ \text{Percentage Modulation} = m \times 100\% \]
- Substituting the value of \( m \):
\[ \text{Percentage Modulation} = \frac{1}{4} \times 100\% = 25\% \]

6. **Conclusion**:
- The percentage modulation of the audio signal is \( 25\% \).

### Final Answer:
The percentage modulation is \( 25\% \).

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