1. Make Background service

package service;

import android.app.Service;
import android.content.Context;
import android.content.Intent;
import android.media.AudioManager;
import android.media.MediaPlayer;
import android.os.IBinder;
import android.support.annotation.Nullable;
import java.io.IOException;


public class BackgroundSoundService extends Service {

    MediaPlayer mPlayer = null;
    private final static int MAX_VOLUME = 100;
    Context context;
    AudioManager.OnAudioFocusChangeListener afChangeListener;


    @Nullable
    @Override
    public IBinder onBind(Intent intent) {
        return null;
    }

    @Override
    public int onStartCommand(Intent intent, int flags, int startId) {

        int musicflag = (int) intent.getExtras().get("songindex");
        if (musicflag == 1) {
            playMusic(R.raw.s1_pondambience);
        } else {
            playMusic(R.raw.s2_integrative_music);
        }
        return Service.START_REDELIVER_INTENT;
    }

    @Override
    public void onDestroy() {
        super.onDestroy();
        if (mPlayer != null) {
            try {
                mPlayer.stop();
                mPlayer.release();
            } finally {
                mPlayer = null;
            }
        }
    }

    public void onTaskRemoved(Intent rootIntent) {
        stopSelf();
    }

    /*
    * playmusic custom method for manage two different background sounds for application
    * */

    public void playMusic(int musicFile) {
        if (mPlayer != null) {
            if (mPlayer.isPlaying()) {
                try {
                    mPlayer.stop();
                    mPlayer.release();
                    mPlayer = MediaPlayer.create(this, musicFile);

                    AudioManager am = (AudioManager) getApplicationContext().getSystemService(Context.AUDIO_SERVICE);
                    int result = am.requestAudioFocus(afChangeListener, AudioManager.STREAM_MUSIC, AudioManager.AUDIOFOCUS_GAIN);

                    if (result == AudioManager.AUDIOFOCUS_REQUEST_GRANTED) {
                        // Start playback.
                        mPlayer.setLooping(true);
                        final float volume = (float) (1 - (Math.log(MAX_VOLUME - 85) / Math.log(MAX_VOLUME)));
                        mPlayer.setVolume(volume, volume);
                        mPlayer.start();
                    }

                } catch (Exception e) {
                    e.printStackTrace();
                }
            } else {
                try {
                    mPlayer = MediaPlayer.create(this, musicFile);

                    AudioManager am = (AudioManager) getApplicationContext().getSystemService(Context.AUDIO_SERVICE);
                    int result = am.requestAudioFocus(afChangeListener, AudioManager.STREAM_MUSIC, AudioManager.AUDIOFOCUS_GAIN);

                    if (result == AudioManager.AUDIOFOCUS_REQUEST_GRANTED) {
                        // Start playback.
                        mPlayer.setLooping(true);
                        final float volume = (float) (1 - (Math.log(MAX_VOLUME - 85) / Math.log(MAX_VOLUME)));
                        mPlayer.setVolume(volume, volume);
                        mPlayer.prepare();
                        mPlayer.start();
                    }
                } catch (IOException e) {
                    e.printStackTrace();
                }

            }
        } else {
            try {
                mPlayer = MediaPlayer.create(this, musicFile);

                AudioManager am = (AudioManager) getApplicationContext().getSystemService(Context.AUDIO_SERVICE);
                int result = am.requestAudioFocus(afChangeListener, AudioManager.STREAM_MUSIC, AudioManager.AUDIOFOCUS_GAIN);

                if (result == AudioManager.AUDIOFOCUS_REQUEST_GRANTED) {
                    // Start playback.
                    mPlayer.setLooping(true);
                    final float volume = (float) (1 - (Math.log(MAX_VOLUME - 85) / Math.log(MAX_VOLUME)));
                    mPlayer.setVolume(volume, volume);
                    mPlayer.start();
                }

            } catch (Exception e) {
                e.printStackTrace();
            }
        }
    }

    /*
    * MediaPlayer methods
    * */

    public void pauseMusic() {
        if (mPlayer.isPlaying()) {
            mPlayer.pause();
            length = mPlayer.getCurrentPosition();

        }
    }

    public void resumeMusic() {
        if (mPlayer.isPlaying() == false) {
            mPlayer.seekTo(length);
            mPlayer.start();
        }
    }

    public void stopMusic() {
        mPlayer.stop();
        mPlayer.release();
        mPlayer = null;
    }

    public boolean onError(MediaPlayer mp, int what, int extra) {
        if (mPlayer != null) {
            try {
                mPlayer.stop();
                mPlayer.release();
            } finally {
                mPlayer = null;
            }
        }
        return false;
    }

}

and start and stop service whenever you want.

2. To Start Service use below method

 private void startBackMusic() {
        Intent musicintent = new Intent(MenuActivity.this, BackgroundSoundService.class);
        musicintent.putExtra(EXTRA_SONGINDEX, 1);
        startService(musicintent);
    }

3. To Stop Service use below method

 private void stopBackMusic() {
          Intent musicintent = new Intent(MenuActivity.this, BackgroundSoundService.class);
            stopService(musicintent);
    }

 @Override
    public void onCreate (){
      super.onCreate();

       Player = MediaPlayer.create(this, R.raw.jingle);
       mPlayer.setOnErrorListener(this);

       if(mPlayer!= null)
        {
            mPlayer.setLooping(true);
            mPlayer.setVolume(100,100);
        }


        mPlayer.setOnErrorListener(new OnErrorListener() {

      public boolean onError(MediaPlayer mp, int what, int
          extra){

            onError(mPlayer, what, extra);
            return true;
        }
          });
    }

If you have not very much activities, You can manage this task by adding boolean flags in activities, where you want music to be played.
When you stop one Activity these flags will show you, whether other Activities need your MediaPlayer

So in your main Activity:

public class MainActivity extends Activity {

    static MediaPlayer introPlayer;
    static boolean sActive;

    @Override
    protected void onResume() {

    // starting the player if it is not playing
        if (!introPlayer.isPlaying()) {
            introPlayer.start();
            introPlayer.setLooping(true);
        }

        // true when activity is active
        sActive = true;
        super.onResume();
    }

    @Override
    protected void onPause() {

        sActive = false;
        super.onPause();
    }

    @Override
    protected void onStop() {

        // before stoping mediaplayer checking whether it is not used by other          activities

        if (introPlayer.isPlaying()
                && !(Activity2.sActive || Activity3.sActive)) {
            introPlayer.pause();
        }

        super.onStop();

    }
}

Other activities:

public class Activity2 extends Activity {

    static boolean sActive;

    @Override
    protected void onPause() {
        sActive = false;

        super.onPause();
    }

    @Override
    protected void onStop() {

        // pausing the player in case of exiting from the app
        if (MainActivity.introPlayer.isPlaying() && !(MainActivity.sActive || Activity3.sActive)) {
            MainActivity.introPlayer.pause();
        }

        super.onStop();
    }

    @Override
    protected void onResume() {
        sActive = true;

        if (!MainActivity.introPlayer.isPlaying()) {
            MainActivity.introPlayer.start();
            MainActivity.introPlayer.setLooping(true);
        }

        super.onResume();
        }
}

And

public class Activity3 extends Activity {

    static boolean sActive;

    @Override
    protected void onPause() {
        sActive = false;

        super.onPause();
    }

    @Override
    protected void onStop() {

        // pausing the player in case of exiting from the app
        if (MainActivity.introPlayer.isPlaying() && !(MainActivity.sActive || Activity2.sActive)) {
            MainActivity.introPlayer.pause();
        }

        super.onStop();
    }

    @Override
    protected void onResume() {
        sActive = true;

        if (!MainActivity.introPlayer.isPlaying()) {
            MainActivity.introPlayer.start();
            MainActivity.introPlayer.setLooping(true);
        }

        super.onResume();
        }
}