The answer below considers the use of a command line program, as done in the question (for Windows). Another approach would be to use a C library to play MP3. Certainly there is some.
The first step is to install an MP3 player that can be triggered by the command line. There are several, one of them is mpg123.
If you are in a Debian-based distribution, you can install mpg123, like this:
sudo apt-get install mpg123
When you do this, you call it via the command line:
mpg123 nomeDaMusica.mp3 &
O & in the line is used so that its command line does not remain locked waiting for the return of the command.
In your C code, you do this:
#include<stdio.h>
#include<stdlib.h>
int main (){
system("mpg123 Rachmaninoff\ -\ Prelude\ in\ C-sharp\ minor.mp3 &");
return 0;
}
Note that the name of the MP3 file is: Rachmaninoff - Prelude in C-sharp minor.mp3
However, for bash dealing with spaces it is necessary to use the \
break character.