An Amplitude Modulated (AM) wave is represented by the expression where a 10kHz sinusoidal message signal modulates a 1MHz carrier signal. The peak carrier amplitude is 10 V and the peak message amplitude is 6V.

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Asked on July 8, 2026Computer Science

This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.

Accepted Answer · 2026-07-08T17:26:20.216Z

Here's the solution for question 1a: a) An Amplitude Modulated (AM) wave is represented by the expression where a 10kHz sinusoidal message signal modulates a 1MHz carrier signal. The peak carrier amplitude is 10 V and the peak message amplitude is 6V. (i) Calculate the Modulation Index (m) of the wave. Step 1: Identify the given amplitudes. Peak carrier amplitude, A_c = 10 V. Peak message amplitude, A_m = 6 V. Step 2: Apply the formula for the modulation index. The modulation index m is given by the ratio of the peak message amplitude to the peak carrier amplitude. m = (A_m)/(A_c) m = 6 V10 V m = 0.6 The modulation index is 0.6. (ii) Determine the Upper Sideband (USB) and Lower Sideband (LSB) frequencies. Step 1: Identify the given frequencies. Message signal frequency, f_m = 10 kHz = 10 × 10^3 Hz. Carrier signal frequency, f_c = 1 MHz = 1 × 10^6 Hz. Step 2: Calculate the Upper Sideband (USB) frequency. The USB frequency is the sum of the carrier frequency and the message frequency. f_USB = f_c + f_m f_USB = 1 × 10^6 Hz + 10 × 10^3 Hz f_USB = 1,000,000 Hz + 10,000 Hz f_USB = 1,010,000 Hz = 1.01 MHz Step 3: Calculate the Lower Sideband (LSB) frequency. The LSB frequency is the difference between the carrier frequency and the message frequency. f_LSB = f_c - f_m f_LSB = 1 × 10^6 Hz - 10 × 10^3 Hz f_LSB = 1,000,000 Hz - 10,000 Hz f_LSB = 990,000 Hz = 0.99 MHz The Upper Sideband frequency is 1.01 MHz and the Lower Sideband frequency is 0.99 MHz. (iii) Calculate the total power transmitted if the antenna resistance is 50Ω. Step 1: Identify the given values and the modulation index from part (i). Peak carrier amplitude, A_c = 10 V. Antenna resistance, R = 50 . Modulation index, m = 0.6. Step 2: Calculate the carrier power (P_c). The carrier power is given by P_c = (A_c^2)/(2R). P_c = (10 V)^22 × 50 P_c = 100 V^2100 P_c = 1 W Step 3: Calculate the total transmitted power (P_t). The total transmitted power for an AM wave is given by P_t = P_c (1 + (m^2)/(2)). P_t = 1 W (1 + ((0.6)^2)/(2)) P_t = 1 W (1 + (0.36)/(2)) P_t = 1 W (1 + 0.18) P_t = 1 W (1.18) P_t = 1.18 W The total power transmitted is 1.18 W. Send me the next one 📸

Accepted Answer · 2026-07-08T17:26:20.216Z

Here's the solution for question 1a: a) An Amplitude Modulated (AM) wave is represented by the expression where a 10kHz sinusoidal message signal modulates a 1MHz carrier signal. The peak carrier amplitude is 10 V and the peak message amplitude is 6V. (i) Calculate the Modulation Index (m) of the wave. Step 1: Identify the given amplitudes. Peak carrier amplitude, A_c = 10 V. Peak message amplitude, A_m = 6 V. Step 2: Apply the formula for the modulation index. The modulation index m is given by the ratio of the peak message amplitude to the peak carrier amplitude. m = (A_m)/(A_c) m = 6 V10 V m = 0.6 The modulation index is 0.6. (ii) Determine the Upper Sideband (USB) and Lower Sideband (LSB) frequencies. Step 1: Identify the given frequencies. Message signal frequency, f_m = 10 kHz = 10 × 10^3 Hz. Carrier signal frequency, f_c = 1 MHz = 1 × 10^6 Hz. Step 2: Calculate the Upper Sideband (USB) frequency. The USB frequency is the sum of the carrier frequency and the message frequency. f_USB = f_c + f_m f_USB = 1 × 10^6 Hz + 10 × 10^3 Hz f_USB = 1,000,000 Hz + 10,000 Hz f_USB = 1,010,000 Hz = 1.01 MHz Step 3: Calculate the Lower Sideband (LSB) frequency. The LSB frequency is the difference between the carrier frequency and the message frequency. f_LSB = f_c - f_m f_LSB = 1 × 10^6 Hz - 10 × 10^3 Hz f_LSB = 1,000,000 Hz - 10,000 Hz f_LSB = 990,000 Hz = 0.99 MHz The Upper Sideband frequency is 1.01 MHz and the Lower Sideband frequency is 0.99 MHz. (iii) Calculate the total power transmitted if the antenna resistance is 50Ω. Step 1: Identify the given values and the modulation index from part (i). Peak carrier amplitude, A_c = 10 V. Antenna resistance, R = 50 . Modulation index, m = 0.6. Step 2: Calculate the carrier power (P_c). The carrier power is given by P_c = (A_c^2)/(2R). P_c = (10 V)^22 × 50 P_c = 100 V^2100 P_c = 1 W Step 3: Calculate the total transmitted power (P_t). The total transmitted power for an AM wave is given by P_t = P_c (1 + (m^2)/(2)). P_t = 1 W (1 + ((0.6)^2)/(2)) P_t = 1 W (1 + (0.36)/(2)) P_t = 1 W (1 + 0.18) P_t = 1 W (1.18) P_t = 1.18 W The total power transmitted is 1.18 W. Send me the next one 📸

An Amplitude Modulated (AM) wave is represented by the expression where a 10kHz sinusoidal message signal modulates a 1MHz carrier signal. The peak carrier amplitude is 10 V and the peak message amplitude is 6V.

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An Amplitude Modulated (AM) wave is represented by the expression where a 10kHz sinusoidal message signal modulates a 1MHz carrier signal. The peak carrier amplitude is 10 V and the peak message amplitude is 6V.

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