Final answer:
The amplitude modulated signal has a carrier frequency at 100 Hz and sidebands at 70 Hz, 90 Hz, 110 Hz, and 130 Hz. The modulated signal's spectrum will include the carrier at 110 V and sidebands' amplitudes calculated based on the modulation index and message amplitudes: 7.2 V and 6.4 V.
Step-by-step explanation:
The question pertains to an amplitude modulated (AM) signal produced by a Double Sideband with Carrier (DSB+Carrier) AM modulator. With a carrier signal c(t) = 110 cos(200πt) and a modulation index of 0.8, the resulting modulated signal will contain a set of upper and lower sidebands created by modulating the carrier with the message signal m(t) = 9 cos(20πt) + 8 cos(60πt).
Frequency Components and Amplitudes:
- The carrier frequency is 100 Hz (since 200πt implies a frequency f where f = ω/2π = 100 Hz).
- The message signal frequencies are 10 Hz and 30 Hz, respectively.
- The sidebands will appear at frequencies fc ± fm, where fc is the carrier frequency and fm is a message signal frequency.
- Using the modulation index of 0.8, the sidebands' amplitudes are calculated as 0.8 times the corresponding message signal amplitude. Therefore, the amplitudes for the sidebands will be 7.2 V at 90 Hz and 110 Hz as well as 6.4 V at 70 Hz and 130 Hz.
The amplitude spectrum will show these frequencies with peaks at the carrier frequency 100 Hz, and sidebands at 70 Hz, 90 Hz, 110 Hz, and 130 Hz with their respective amplitudes as mentioned above. The carrier amplitude will be 110 V.