Say you want to send a message out on the airwaves. How do you do it? Well, sound is a wave, right? And radio is a wave too, right? So why not just convert the sound waves of your message directly into radio waves and broadcast that signal? There are a couple of problems with that. The human ear can hear sounds ranging in frequency from 20 Hz to 20,000 Hz. This means that your signal will have a similar range. But where in that range will it fall? As it turns out, it'll be all over the place, unless you plan on sending out A above middle C all day. The waveform of a human voice looks something like this:

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There's no well-defined frequency there. It changes with time. And it's pretty hard to tune your radio to a signal with a frequency that is changing drastically all the time. Moreover, these are fairly low frequencies, at least when we're talking about radio signals. It's hard to get an antenna to transmit at 20,000 Hz, much less 20 Hz. So what's the solution? Use a carrier wave. A carrier wave is a wave with a frequency far higher than that of the signal (and I mean far higher — for AM radio, frequencies around one million Hz are often used!) which is used to transmit the signal. This is done through the process of modulation. Modulation is, in essence, a process in which a certain property of the carrier wave is multiplied by the signal. It's...well, perhaps we'd be better off with some pictures at this point. Say that this is the signal that we want to send:


                                          .
                                                 .',!¦=CJC7=7JJCC=¦!'.
                                              .,¦7CC=!,'........,!¦=C7¦*'.
                                           '*=CC(!'                 .,¦=7C=,.
                                        .,(CC(*.                       .'*=7=*'.
                                      .!7J7!'                              '¦7C=*.
                                    .¦JC¦,.                                  .,¦CC*.
                                  .!3J!.                                        '¦3C*.
                                '!JC¦.                                            '¦CC!'
                              .!CJ¦.                                                .!JC!.
                            .!7C¦'                                                    '!CC*.
                           'J3¦'                                                        ,(C7'
                         '¦$¦'                                                            '(37,
                       .¦JJ!                                                                ,=J¦.
                     .*7J!                                                                    ,7C¦'                                                                            ..
                    .(J7,                                                                      .!77*.                                                                        .,(*
                    '¦,.                                                                         .!7=*                                                                      '=3('
                                                                                                   '¦7=*.                                                                 '!77!.
                                                                                                     .!J7,                                                              .!JC!.
                                                                                                       '¦C(,.                                                         .*JJ!.
                                                                                                         '(7('                                                      .*=3('
                                                                                                           '(C(,.                                                 .*CJ¦'
                                                                                                            .*=C=,                                               ,7J=,
                                                                                                               '¦CC!.                                         .!7C(,
                                                                                                                 ,(JC!.                                     .*C3(,.
                                                                                                                   .*=C=*.                               .*=JJ,
                                                                                                                      '(CC(,.                         .,(JJ=,.
                                                                                                                        .*=C7(!,.                 .'*(CJ7!.
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                                                                                                                              .',!(7====(((¦===((¦*'.
                                                                                                                                   ...'',,,,'...
                                                                                                                                                                            ..

And say this is our carrier wave:*



                      ..      .'    . .'      '.      ''      ,'     .,'     .,'     .*'     .,'     .!,     .!,     .!,     .(*     '¦,     '¦,     '7,     ,(,     '(*     'C,
                      7C.    .=J,    .JJ.    .CC.    'C7.    'AC     ,$=.    ,AJ.    ,A7     ,$C.    '5J.    *57     *AC.    ,@J.    (#7.    ¦57     !M7     =#=.    ¦#7     !W7
                     .AÐ'    '$#!    'Ð@*    ,5#'    *#A,    *M5.    ¦@$'    *ÐA,    ,Ð#     ¦@%,    ,ÐA'    !Ð5.    (Ð%,    *W%.    C@3.   .=Ð3.    (W$.   .C@C.   .=ÐJ.    ¦@3
                     ,5Ð!    'J5(    '#5¦    ¦5#,    !5A!    ¦@#'    =A$,    !5A*    *5@.    ¦%$*    ,A%*    ¦%5.   .=5$*    ¦5A,    7$3.   .7#3'    7J5'   .C%J'   .7AJ'    =C5.
                     !%%=    *7%7.   'AJ(    =35!   .¦33(    (J$,   .73$*   .¦33¦    ¦7A'   .=7C!    ¦JC¦    ==%'   .=JC!    CC3,    C7$'   '=3J*   .3!5,   .7C3,   '7JJ*    J!#'
                     ¦JJC    ¦C37.   *3=7    ==$(   .=JJ7    77J¦   .=(J!   .7CJ7    C¦J!   .=(7¦   .=C77    7¦J!   .=7C¦    3=7!   .3(3,   '=7C!   .$!A!   'C=J,   '=(C¦   .3*5,
                     ¦7¦%.   ¦=77'   !7¦C    C(3C.  'C7C7    3===   .7(J¦.  .7=77    J!7!   .7(C(.   (=(7    J¦7¦   '7=J=.  .3!=7   'C!J*   ,7¦7¦   ,%'J¦   ,C¦J!   'C!7¦   ,3'J*
                     =(*A.  .(=!('   (7!3'   J¦7J.  'J===.  .$¦7J.  '7!C=.  '7(=C   .J*7C   '=!(¦.  .C(¦=   .J*=C   ,=!C=.  'A*=7   ,C*J¦   ,7*=(   *A'C(   !C*J¦.  ,J,=(   ,3'C¦
                     7(,A.  .(=¦7,   J(!3'  .C¦!J.  '3=(7.  '$,=3.  '7!==.  'C!7J.  'J,(C   '7!¦¦.  .C,¦7.  '3*(C   ,7!=7'  '$,=J   !C,C(   *J,7=.  !A'C=   ¦C*J=.  ,3,==   ,J.=7
                     J('5'  .((!C*   3(,3,  .J¦,3.  ,J¦(C'  '$,¦A'  *7*(7.  'J,¦C'  '3,,3.  ,=*!='  .C'*7'  'J**$.  *C*(='  '%'(J   ¦C,¦=   *J'==.  !J.77   ¦='77.  '7.=7.  !J.!7
                     C¦.%,  .==,7*  .$!,3!  .J¦,A.  ,3!¦7,  *%'*%'  *7*!J'  ,$'!7'  *3'.$.  ,=**7'  '3.*C,  !C',%.  *C*!7'  ,5.!C.  (7'!J.  *J'(=.  ¦$.¦J.  ((.=7.  ,C.¦=.  ¦J.*C
                     3¦.C*  '7('J(. .%*'C!  'J!'A'  ,$*!3!  !A.'$,  !C*,C'  ,3.!J*  !3..%'  *7,,C,  '$ *J!  ¦J'.$.  !J,!C,  ,% *J,  (7'*3.  ¦C.¦='  ¦J !J.  (7'!C.  !J.¦='  ¦7.*3.
                    '3¦.J(  '=¦.C(. .%*.(¦  *C*.%!  ,J,*J!  !%.'$*  ¦7,,$,  ,3.!J!  !J..$,  !C,,3*  ,% ,C!  !C' 3'  !J'!3*  *$ ,J,  ¦(.,$. .¦C.¦C,  ¦C ,J'  (=.*C.  !C.¦C,  (=.,$'
                    .3! CC  ,7! 7=. .$'.==  *C* J=  *$''C(  *$.'$!  ¦C,.J,  *3.,J(  *=..3,  ¦C,'J*  *% 'C(  !7' $,  !J,*J!  !C 'C!  =(.'5' .(3.!C*  C( ,3,  ((.,3'  !J.!7,  7( .3'
                    '3! =J  ,C! =7' '$..=J  !C, C=  *%'.C=. !3..C=  ¦7'.J*  !%.'C=  ¦=. 7¦  !C,.C¦. *A..==  (C' C¦  *7''C¦  !C '=¦ .7=..%* .77 ,C!  == '3* .=¦.'3'  !7 ,7!  7=..3,
                    ,J* *$. ,C* =7' ,%  ¦C  ¦C, 7C  *$'.7=. ¦7 .=7  ¦='.J(  ¦J..=(  =C. ((  !7' C=. !J .(=  =C' =¦  !C'.C(. !J .¦¦ .C¦ .%! .7= ,J¦  3¦ 'C! .7¦ .J, .== '7¦  3¦ .C*
                    ,J* ,$. *J, ¦=' ,$  !C. ¦C, =C  !3. ==. (= .=J .(=. J( .=C  (=. =C. (7  ¦=. (¦. (C  ¦=  (7' (C  ¦7. 7(. ¦J .¦( .C¦ .$= .== '7¦  %¦ .=¦ 'C¦ .3! .7! '=¦  $! .=! .,'
                    .*. '$' !3, !7' *%  !J' ¦=' !J .($. (=' == .(3 .=(. ==..7C  (7. 7(. =J  ¦(. ¦=. (C  ¦=. 7=. *3 .¦=  ==. =C .(7 .J¦  J( .==  =(. $¦ .== 'J( .C! .7¦  ((. $! .== '=¦
                         %, *J, *C, !A  *C' (=' '$..¦C. ¦C, J=  ¦J..7=. ¦7. ¦=  ¦=' C¦. !J .¦(. ¦J' !=  !7' C=. ,3..(=  (7' =( .(C .J¦  (C '7¦  =(. $! .(7 'C¦  (= 'J¦  =7. J*  ¦7 ,C¦
                         $* !3, ,J* !$  ,C* ((. .5' !C. *7, C=  *3''C=. !J..(=  !=' C¦  ,3'.((  *J' ¦=  *='.C¦. '$'.==  ¦C' C¦ .¦7 'J¦  !J 'C*  ==' %! .¦7 ,7!  (C.'J,  (7. J*  != *C!
                         C! !J' 'J* *C  ,C! =='  5,.=7  *C* 7¦  *3,'C=  'J..J(  *=, J*  'J''7=  'J' J¦  *=,.3!  ,$''7=  *7' $*  !7.'C*  !3.'7,  ¦=''$,  !J.*7*  ¦J.'J,  !('.C'  ¦J.*7,
                         7! ¦C. 'J! !J  '7¦.7(.  A,.==  *J! 3¦  ,3*,J(  '$'.J!  !C* 3!  'J,'7(  '$' J¦  *C!.3¦  .3,'7¦  ,7'.$,  *C''J!  '%',J'  ¦7''$,  !C.*C*  ,C.,$.  !=''J,  !J.*7,
                         =C.¦7. .C¦.((  .¦('3(   A!.C=  ,C! $!  'J*,7!  'A'.3!  *C* J*  .7,,7¦  'A, 3!  ,7¦.C*   3,,7*  '3,.$,  ,=,,=,  .%'*3,  !J**3'  *C'*7,  'C.*$.  ¦J**J,  ,J'*=,
                         ¦J.¦7.  7=.7(  .¦='J(   $¦'J¦  '7!.3*  'C¦,7!  'A,'3,  '7!.C,  .=!'=!  .$,.3*  '7(.C*   J*,7*  .C,'%'  ,=**7,   A,*$'  *C*!3'  ,C,!=,  .$'*$   *=,!C'  ,J'!C'
                         !J.(7.  =7.J¦   ¦7,J¦   77'J¦  .7¦'$*  .==*7,  .3*'%*  '=¦,C,  .(('(*  .C!.$*  .=(,C*   =¦,=,  .C!,%'  '(¦*=,   3,!$.  ,J!¦3.  '7!!7'   3,!$   ,7!¦C'  'J*¦C'
                         *3,7=   ¦7'3¦   ¦7*J¦   =3,J*  .7=*3,  .(7!C*   C¦,$'  .=(*C'  .¦=*7*   7¦,$'   (=*C*   (7,C,  .C¦¦%.  .¦(¦='   J!!$.  'C!=C.  .(¦¦='   $!!$   '7!(=.  .7!¦C.
                         ,$*J=   *C,$!   ¦3!C!   ¦3*$,   ((¦$,  .=J!C,   ==*%.   ((!C'   !7*7'   (=*$.   (7¦7,   ¦J*C'   =(¦A.   ¦7(7'   C=*J.  .7¦7C.  .¦=(=.   3¦¦3   .7=7=.  .((¦=.
                         .3!C¦   ,3*%*   !J(C*   ,%!$,   !7=$'   ¦J¦C,   ¦J*$    ¦=7J'   *7!J'   !J*3    ¦7=C,   *J!3'   ¦7¦J    ¦C=7'   =C!C    =(=7.   !7(=.   77=3    ==7¦.  .¦J(=.
                         .3(C!   .$¦%,   *JJJ*   .%¦3.   *CC3'   ¦$=C,   *3!3    !=C7'   *C(J'   ,3¦$    !77C'   ,J($.   *7=J    !CJ7'   ¦$¦=    (=J(    !J7(    (JJ3    (73¦.   ¦$=!
                         .7CJ,   .J7%.   ,C$J,    $=%.   ,$%7.   *JCC'   '3(7    *C3(.   ,C7C.   .$7J    *C37'   '3J3.   'CJ(    *3A=.   *%3=    !JA!    !$3(    ,3%(    ¦JA!    !$C(
                         .=5%,   .C$%.   .=#3,    $%3    '35=.   'C%7.    $A=    ,CA¦.   'C%7.    3#C    'C5(.   .3ÐJ.   .3@(    ,3A(    'A#(    *5Ð!    *$%¦    .A@¦    !A@!    ,$%¦
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                          '7(     .C¦     '¦*     '7,     ,7,     '!'     '(.     ,('     '¦'     '!.     '*'     '!.     '*.     ',.     .,      ,,      .'      .'      .'      .'
                           ..      ..      .       .       .               .       .




Then this would then be the form of the signal that was actually sent out if the process of amplitude modulation were used to piggyback the signal on the carrier:


                                                                                                                                                                                         .
                                                      .,'     .J,     .*.
                                                      !%=     ,W7     ¦A¦
                                                      ¦@J.    !©C     =@=.
                                              '7!     !#3.    !©J     =Ð7.    ,7!
                                              *#C.    !#3'    =M%.    7ÐC.    ¦@C
                                              ,#%.   .(#3,    J$$'    =$C.    ¦Ð3      .
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Hopefully that gets the idea across. Mind you, there are other kinds of modulation out there — amplitude modulation was just the first to be used, and when it comes to explaining what a carrier wave is, it's also the most pedagogically valuable. The details of modulation are best left for another node.

*NB: This is not to scale at all — carrier waves generally have wavelengths hundreds of times shorter than the signal they carry.

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