Tricky situation with race condition

I have this race condition with an audio playback class, where every time I start playback I set keepPlaying as true, and false when I stop.

The problem happens when I stop() immediately after I start, and the keepPlaying flag is set to false, then reset to true again.

I could put a delay in stop(), but I don't think that's a very good solution. Should I use conditional variable to make stop() wait until keepPlaying is true?

How would you normally solve this problem?

#include <iostream>
#include <thread>
using namespace std;


class AudioPlayer

{
    bool keepRunning;
    thread thread_play;

    public: 
    AudioPlayer(){ keepRunning = false; }
    ~AudioPlayer(){ stop(); }

    void play()
    {
        stop();
        // keepRunning = true; // A: this works OK
        thread_play = thread(&AudioPlayer::_play, this);
    }
    void stop()
    {
        keepRunning = false;
        if (thread_play.joinable()) thread_play.join();
    }
    void _play()
    {
        cout << "Playing: started\n";
        keepRunning = true; // B: this causes problem
        while(keepRunning)
        {
            this_thread::sleep_for(chrono::milliseconds(100)); 
        }
        cout << "Playing: stopped\n";
    }
};


int main()
{
    AudioPlayer ap;

    ap.play();
    ap.play();
    ap.play();

    return 0;
}

Output:

$ ./test
Playing: started
(pause indefinitely...)