Question:
A message signal of frequency \(8\ \text{kHz}\) and peak voltage \(12\ \text{V}\) is used to modulate a carrier of frequency \(1.2\ \text{MHz}\) and peak voltage \(20\ \text{V}\). The modulation index is
A message signal of frequency \(8\ \text{kHz}\) and peak voltage \(12\ \text{V}\) is used to modulate a carrier of frequency \(1.2\ \text{MHz}\) and peak voltage \(20\ \text{V}\). The modulation index is
Show Hint
For amplitude modulation:
\[
m=\frac{V_m}{V_c}
\]
where \(V_m\) is the modulating signal amplitude and \(V_c\) is the carrier signal amplitude.
For proper modulation,
\[
0\leq m\leq 1
\]
Updated On: Jun 25, 2026
- \(0.2\)
- \(0.3\)
- \(0.4\)
- \(0.6\)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Recall the formula for modulation index.
In amplitude modulation (AM), modulation index is given by \[ m=\frac{V_m}{V_c} \] where \[ V_m=\text{peak voltage of modulating signal} \] and \[ V_c=\text{peak voltage of carrier wave} \]
Step 2: Identify the given values.
Given: \[ V_m=12\ \text{V} \] and \[ V_c=20\ \text{V} \]
Step 3: Calculate the modulation index.
Substituting the values, \[ m=\frac{12}{20} \] \[ m=0.6 \]
Step 4: Final conclusion.
Hence, the modulation index is \[ \boxed{0.6} \]
In amplitude modulation (AM), modulation index is given by \[ m=\frac{V_m}{V_c} \] where \[ V_m=\text{peak voltage of modulating signal} \] and \[ V_c=\text{peak voltage of carrier wave} \]
Step 2: Identify the given values.
Given: \[ V_m=12\ \text{V} \] and \[ V_c=20\ \text{V} \]
Step 3: Calculate the modulation index.
Substituting the values, \[ m=\frac{12}{20} \] \[ m=0.6 \]
Step 4: Final conclusion.
Hence, the modulation index is \[ \boxed{0.6} \]
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