Audio sine waves of 3 kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz.Which of the following statements are true?

The side band frequencies are 1506 kHz and 1494 kHz.

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The bandwidth required for amplitude modulation is 6 kHz

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The bandwidth required for amplitude modulation is 3 kHz

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The side band frequencies are 1503 kHz and 1497 kHz.

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Solution

The correct options are
B The bandwidth required for amplitude modulation is 6 kHz
D The side band frequencies are 1503 kHz and 1497 kHz.
Side band frequencies: The AM wave contains three frequencies $f_{c}, (f_{c} + f_{m})$ and $(f_{c} - f_{m})$ where $f_{c}$ is called carrier frequency, $(f_{c} + f_{m})$ and $(f_{c} - f_{m})$ are called side band frequencies.
$(f_{c} + f_{m})$ : is upper side band (USB) frequency
$(f_{c} - f_{m})$ : is the lower side band (LSB) frequency
Side band frequencies are generally close to carrier frequency.
According to the given criteria,
frequency of audio sine wave $f_{m} = 3 k H z$ and frequency of carrier signal $f_{c} = 1.5 M H z = 1500 k H z$
Now, side band frequencies is
$f_{c} \pm f_{m} = (1500 \pm 3) ⟹ = 1503 k H z, 1497 k H z$
Upper side Band frequency is 1503kHz
and Lower side band frequency is 1497kHz
Also bandwidth is $2 f_{m} = 2 \times 3 = 6 k H z$

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