Solution

You can now use base64 files to produce sounds when imported as data URI. The solution is almost the same as the previous ones, except you do not need to import an external audio file.

function beep() {
    var snd = new Audio("data:audio/wav;base64,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");  
    snd.play();
}
beep();

Compatibility

Data URI is supported on almost every browser now. More information on

Demo

Conversion Tool

And here is where you can convert mp3 or wav files into Data URI format:

/*if you want to beep without using a wave file*/
var context = new AudioContext();
var oscillator = context.createOscillator();
oscillator.type = "sine";
oscillator.frequency.value = 800;
oscillator.connect(context.destination);
oscillator.start(); 
// Beep for 500 milliseconds
setTimeout(function () {
    oscillator.stop();
}, 100);                
            

The top answer was correct at the time but is now wrong; you can do it in pure javascript. But the one answer using javascript doesn't work any more, and the other answers are pretty limited or don't use pure javascript.

I made my own solution that works well and lets you control the volume, frequency, and wavetype.

//if you have another AudioContext class use that one, as some browsers have a limit
var audioCtx = new (window.AudioContext || window.webkitAudioContext || window.audioContext);

//All arguments are optional:

//duration of the tone in milliseconds. Default is 500
//frequency of the tone in hertz. default is 440
//volume of the tone. Default is 1, off is 0.
//type of tone. Possible values are sine, square, sawtooth, triangle, and custom. Default is sine.
//callback to use on end of tone
function beep(duration, frequency, volume, type, callback) {
    var oscillator = audioCtx.createOscillator();
    var gainNode = audioCtx.createGain();
    
    oscillator.connect(gainNode);
    gainNode.connect(audioCtx.destination);
    
    if (volume){gainNode.gain.value = volume;}
    if (frequency){oscillator.frequency.value = frequency;}
    if (type){oscillator.type = type;}
    if (callback){oscillator.onended = callback;}
    
    oscillator.start(audioCtx.currentTime);
    oscillator.stop(audioCtx.currentTime + ((duration || 500) / 1000));
};

Someone suggested I edit this to note it only works on some browsers. However Audiocontext seems to be supported on all modern browsers, as far as I can tell. It isn't supported on IE, but that has been discontinued by Microsoft. If you have any issues with this on a specific browser please report it.

I wrote a function to beep with the new Audio API.

var beep = (function () {
    var ctxClass = window.audioContext ||window.AudioContext || window.AudioContext || window.webkitAudioContext
    var ctx = new ctxClass();
    return function (duration, type, finishedCallback) {

        duration = +duration;

        // Only 0-4 are valid types.
        type = (type % 5) || 0;

        if (typeof finishedCallback != "function") {
            finishedCallback = function () {};
        }

        var osc = ctx.createOscillator();

        osc.type = type;
        //osc.type = "sine";

        osc.connect(ctx.destination);
        if (osc.noteOn) osc.noteOn(0); // old browsers
        if (osc.start) osc.start(); // new browsers

        setTimeout(function () {
            if (osc.noteOff) osc.noteOff(0); // old browsers
            if (osc.stop) osc.stop(); // new browsers
            finishedCallback();
        }, duration);

    };
})();

jsFiddle.

Using Houshalter's suggestion, I made this simple tone synthesizer demo.

Screenshot

Here is a screenshot. Try the live demo further down in this Answer (click Run code snippet).

Demo code

audioCtx = new(window.AudioContext || window.webkitAudioContext)();

show();

function show() {
  frequency = document.getElementById("fIn").value;
  document.getElementById("fOut").innerHTML = frequency + ' Hz';

  switch (document.getElementById("tIn").value * 1) {
    case 0: type = 'sine'; break;
    case 1: type = 'square'; break;
    case 2: type = 'sawtooth'; break;
    case 3: type = 'triangle'; break;
  }
  document.getElementById("tOut").innerHTML = type;

  volume = document.getElementById("vIn").value / 100;
  document.getElementById("vOut").innerHTML = volume;

  duration = document.getElementById("dIn").value;
  document.getElementById("dOut").innerHTML = duration + ' ms';
}

function beep() {
  var oscillator = audioCtx.createOscillator();
  var gainNode = audioCtx.createGain();

  oscillator.connect(gainNode);
  gainNode.connect(audioCtx.destination);

  gainNode.gain.value = volume;
  oscillator.frequency.value = frequency;
  oscillator.type = type;

  oscillator.start();

  setTimeout(
    function() {
      oscillator.stop();
    },
    duration
  );
};

frequency
<input type="range" id="fIn" min="40" max="6000" oninput="show()" />
<span id="fOut"></span><br>
type
<input type="range" id="tIn" min="0" max="3" oninput="show()" />
<span id="tOut"></span><br>
volume
<input type="range" id="vIn" min="0" max="100" oninput="show()" />
<span id="vOut"></span><br>
duration
<input type="range" id="dIn" min="1" max="5000" oninput="show()" />
<span id="dOut"></span>
<br>
<button onclick='beep();'>Play</button>

You can clone and tweak the code here: Tone synthesizer demo on JS Bin

Have fun!

Compatible browsers:

• Chrome mobile & desktop
• Firefox mobile & desktop
• Opera mobile, mini & desktop
• Android browser
• Microsoft Edge browser
• Safari on iPhone or iPad