QJEEM23Ph6908: JEE Main 2023 Physics - Class 12 JEEM23Ph6908 Solution: The amplitude of is modulated by signal. The amplitude…

When an amplitude modulated signal is created, the frequency components of the resulting signal consist of the carrier frequency, the sum, and the difference of the carrier and modulating frequencies.

In this case, the carrier signal is $15 \sin (1000 \pi t)$ , which has a frequency of

$\frac{1000 \pi}{2 \pi} = 500 \mathrm{Hz}$ (Option A).

The modulating signal is $10 \sin (4 \pi t)$ , which has a frequency of $\frac{4 \pi}{2 \pi} = 2 \mathrm{Hz}$ .

Now, we find the sum and difference of the carrier and modulating frequencies:

Sum: $500 \mathrm{Hz} + 2 \mathrm{Hz} = 502 \mathrm{Hz}$ (Option E)

Difference: $500 \mathrm{Hz} - 2 \mathrm{Hz} = 498 \mathrm{Hz}$ (Option D)

So, the amplitude modulated signal contains frequencies of 500 Hz, 2 Hz, 498 Hz, and 502 Hz.

The correct answer is (A, D, and E only).