Beat Notes

The following Matlab code enables you to generate, and listen to, the sum of two audio tones.  Read this blog post for more details. 

%     Filename:  Beat_Frequency.m
%
%     [Richard Lyons, Feb. 2013]
      
clear, clc
 
Fs = 8192; % Sample rate of dig. samples
N = 8192;  % Number of time samples
n = 0:N-1;
 
Wave_1 = sin(2*pi*210*n/Fs);  % First tone, 210 Hz
Wave_2 = sin(2*pi*200*n/Fs);  % Second tone, 200 Hz
 
        % Plot the two tones 
        figure(1)
        plot(n/Fs, Wave_1, '-b')
        ylabel('200 Hz'); xlabel('Time (sec.)'); 
        hold on
        plot(n/Fs, Wave_2, '-r')
        axis([0, 0.05, -1.2, 1.5]); 
        ylabel('Input tones'); xlabel('Time (sec.)'); 
        title('red = 200 Hz tone,  blue = 210 Hz tone'); 
        grid on, zoom on
        hold off
 
Product = Wave_1.*Wave_2;
Sum = Wave_1 + Wave_2;

        % Plot the tones' product and sum 
        figure(2)
        subplot(2,1,1)
        plot(n/Fs, Product, '-b'), 
        ylabel('Product'); xlabel('Time (sec.)'); 
        grid on, zoom on
        hold on
        Red_Curve = 0.5*cos(2*pi*10*n/Fs) + 0.5;  % Used for plotting only
        plot(n/Fs, Red_Curve, '-r')
        axis([0, 0.3, -1.25, 1.5]);
        hold off
        grid on, zoom on
 
        subplot(2,1,2)
        plot(n/Fs, Sum, '-b')
        hold on
        Red_Curve = 2*cos(2*pi*5*n/Fs);  % Used for plotting only
        plot(n/Fs, Red_Curve, '-r')
        axis([0, 0.3, -2.4, 3]);
        hold off
        ylabel('Sum'); xlabel('Time (sec.)');
        grid on, zoom on
 
% Play all the signals
    sound(Wave_1, Fs)
    pause(1.2)
    sound(Wave_2, Fs)
    pause(1.2)
    sound(Product, Fs)
    pause(1.2)
    sound(Sum, Fs)
 
% Spec analysis of the "Sum" signal
Spec = fft(Sum);
Spec_Mag = abs(Spec);
Freq = n*Fs/N; % Freq vector in Hz
 
        figure (3)  % Plot positive-freq spec amg
        plot(Freq(1:N/16), Spec_Mag(1:N/16))
        title('Spec Mag of "Sum" signal')
        ylabel('Mag.'), xlabel('Hz')
        grid on, zoom on