Physics waves amplitude modulationI need help with part (b). I dont quite get what the question is asking. Thank you! Amplitude modulation is a simple form of radio communication. A carrier wave at frequency 𝜔1 is modulated in time with information to give a signal 𝐴(𝑡) cos 𝜔1𝑡. For example NHK broadcasts at 594 kHz in Tokyo and the amplitude modulation 𝐴(𝑡) represents the newsreader’s voice. Inside your radio receiver demodulation is performed by multiplying the detected signal with another signal at 𝜔2 with a relative phase of 𝜙. a. Prove that: cos 𝜔1𝑡 cos(𝜔2𝑡 + 𝜙) = 1/2 (cos((𝜔1 + 𝜔2)𝑡 + 𝜙) + cos((𝜔1 − 𝜔2 )𝑡 − 𝜙) b. Show that the amplitude 𝐴(𝑡) can be recovered through this multiplication if the resulting signal is passed through a “low pass filter” (a low pass filter at 𝜔𝑐 transmits signals with frequency below 𝜔𝑐 and blocks signals above 𝜔𝑐 ). What should the frequencies 𝜔2 and 𝜔𝑐 and the phase 𝜙 be chosen to be to maximise the signal?