An audio signal `v_m = 20 sin 2 pi (1500 t)` amplitude modulates a carrier
` v_C = 80 sin 2pi (100,000t )`. The value of percent modulation is ___

Answer

To find the percent modulation of the given audio signal and carrier wave, we can follow these steps:

### Step 1: Identify the Maximum Values
The audio signal is given by:
\[ v_m = 20 \sin(2 \pi (1500 t)) \]
From this, we can see that the maximum value of the audio signal, denoted as \( A_m \), is:
\[ A_m = 20 \]

The carrier wave is given by:
\[ v_C = 80 \sin(2 \pi (100,000 t)) \]
From this, we can see that the maximum value of the carrier wave, denoted as \( A_C \), is:
\[ A_C = 80 \]

### Step 2: Use the Percent Modulation Formula
The formula for percent modulation is given by:
\[ \text{Percent Modulation} = \left( \frac{A_m}{A_C} \right) \times 100 \]

### Step 3: Substitute the Values
Now, substituting the values of \( A_m \) and \( A_C \) into the formula:
\[ \text{Percent Modulation} = \left( \frac{20}{80} \right) \times 100 \]

### Step 4: Calculate the Result
Calculating the fraction:
\[ \frac{20}{80} = \frac{1}{4} \]
Now, multiplying by 100:
\[ \text{Percent Modulation} = \left( \frac{1}{4} \right) \times 100 = 25 \]

### Final Answer
Thus, the value of percent modulation is:
\[ \text{Percent Modulation} = 25\% \]

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