An amplitude modulated wave is represented by `C_m = 10(1+ 0.2 sin 12560 t ) sin (1.11 x 10^4 t) V`. The modulating frequency in KHz will be

Answer

To find the modulating frequency from the given amplitude modulated wave equation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Equation**:
The amplitude modulated wave is given by:
\[ C_m = 10(1 + 0.2 \sin(12560 t)) \sin(1.11 \times 10^4 t) \, V \]

2. **Recognize the Structure**:
The general form of an amplitude modulated wave can be expressed as:
\[ C_m = A_c(1 + m \sin(2\pi f_m t)) \sin(2\pi f_c t) \]
where \( A_c \) is the carrier amplitude, \( m \) is the modulation index, \( f_m \) is the modulating frequency, and \( f_c \) is the carrier frequency.

3. **Extract the Modulating Frequency**:
From the equation, we can see that the term \( 12560 t \) corresponds to \( 2\pi f_m t \). Thus, we can equate:
\[ 2\pi f_m = 12560 \]

4. **Solve for \( f_m \)**:
Rearranging the equation gives:
\[ f_m = \frac{12560}{2\pi} \]

5. **Calculate \( f_m \)**:
Using \( \pi \approx 3.14 \):
\[ f_m = \frac{12560}{2 \times 3.14} \approx \frac{12560}{6.28} \approx 2000 \, \text{Hz} \]

6. **Convert to Kilohertz**:
Since 1 kHz = 1000 Hz, we convert:
\[ f_m = \frac{2000}{1000} = 2 \, \text{kHz} \]

### Final Answer:
The modulating frequency is \( 2 \, \text{kHz} \).

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