Why is the AM demodulated signal amplified compared to the message signal for some specific frequency values?

Question

I am modulating and demodulating a signal using built-in ammod and amdemod functions of matlab. Fc is set to 500, when I use Fs=2000, the demodulated signal matches up with the message signal very well.

But when I use Fs=1000.. the demodulated signal appears to be amplified. Why is this happening? Is it because of aliasing as the value of Fs is not properly satisfying the Nyquist Cretierion?

For Fs=1000:

Code is as follows:

clc
clear all
close all
pkg load communications



Fc=500;  %Defining parameters for carrier frequency
Fs=1000;  %Defining parameters for sampling rate
Ts=1/Fs;  %Defining sampling period
Tc=1/Fc;

t=0:Ts:1.0239; %%Defining time scale
t2=0:Tc:12;
%%Step 2- Generating the Message an d Carrier Signal
x=3*cos(50*pi*t)-sin(10*pi*t); %%Defining Message signal
Ac=1; %Amplitude of the Carrier Signal
ct=Ac*cos(500*pi*t2); %%carrier signal
%x=x(1:2000);%limiting x to 2000 samples

%%Step 3 - Generating the AM-Signal

x_am = ammod(x,Fc,Fs);

%%Step 4 - Demodulating the AM-Signal

x_dem =amdemod(x_am,Fc,Fs);

Answer 1

The sampling frequency should be higher than 2*(Fc+BW) to fulfil Nyquist criterion, as you said.