Custom MediaStream

I'm receive raw float32 audio through websockets and would like to playback this in the browser. From my understanding I would need to to use MediaStream API for this. However, I cannot find a way to create a MediaStream which I can append data buffers to.

What is the proper way to achieve this?

I'm trying something like this:

    var context = new AudioContext();

    context.sampleRate = 48000;

    var stream = null; // ????

    var source = context.createMediaStreamSource(stream);
    source.connect(context.destination);
    source.start(0);

    socket.onmessage = function (event) {
        stream.appendBuffer(new Float32Array(event.data)); // ????
    };

from Custom MediaStream