Question:
An audio signal \( 10 \sin 2\pi(1500)t \) volt amplitude modulates a carrier \( 40 \sin 2\pi(10^5)t \) volts. The modulation factor and percentage modulation are:
An audio signal \( 10 \sin 2\pi(1500)t \) volt amplitude modulates a carrier \( 40 \sin 2\pi(10^5)t \) volts. The modulation factor and percentage modulation are:
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Always ensure you are using peak amplitudes for \( A_m \) and \( A_c \); if the signal is given in root-mean-square (RMS) values, you must convert them to peak values first, though the ratio will remain the same.
Updated On: Jun 9, 2026
- \( 0.25, 25\% \)
- \( 0.40, 40\% \)
- \( 0.10, 10\% \)
- \( 0.50, 50\% \)
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The Correct Option is A
Solution and Explanation
Concept:
In amplitude modulation (AM), the modulation index (also called modulation factor, \(\mu\)) is defined as the ratio of the amplitude of the modulating (audio) signal, \( A_m \), to the amplitude of the carrier wave, \( A_c \). It is expressed as:
$$ \mu = \frac{A_m}{A_c} $$
The percentage modulation is defined as \( \mu \times 100\% \).
Step 1: Extract amplitudes from the given equations.
The modulating signal equation is \( v_m(t) = 10 \sin(2\pi \cdot 1500 t) \). The peak amplitude \( A_m = 10 \text{ V} \). The carrier wave equation is \( v_c(t) = 40 \sin(2\pi \cdot 10^5 t) \). The peak amplitude \( A_c = 40 \text{ V} \).
Step 2: Calculate the modulation factor \(\mu\).
$$ \mu = \frac{10}{40} = 0.25 $$
Step 3: Calculate percentage modulation.
$$ \% \text{ Modulation} = \mu \times 100\% = 0.25 \times 100\% = 25\% $$ $$\boxed{0.25, 25\%}$$
Step 1: Extract amplitudes from the given equations.
The modulating signal equation is \( v_m(t) = 10 \sin(2\pi \cdot 1500 t) \). The peak amplitude \( A_m = 10 \text{ V} \). The carrier wave equation is \( v_c(t) = 40 \sin(2\pi \cdot 10^5 t) \). The peak amplitude \( A_c = 40 \text{ V} \).
Step 2: Calculate the modulation factor \(\mu\).
$$ \mu = \frac{10}{40} = 0.25 $$
Step 3: Calculate percentage modulation.
$$ \% \text{ Modulation} = \mu \times 100\% = 0.25 \times 100\% = 25\% $$ $$\boxed{0.25, 25\%}$$
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