AudioContext on Safari

  var AudioContext = window.AudioContext // Default
      || (window as any).webkitAudioContext;// Safari and old versions of Chrome

    this.audioContext = new AudioContext();

Browser support limitations

The Web Audio API (id est AudioContext) is not supported by all the browsers. Some browsers may have it prefixed with their vendor prefix, but older browsers do not support it at all. Therefore, to answer your question: you cannot use the AudioContext on all the browsers.

Nonethless, you can still use the Web Audio API on supported browser using feature detection (see below), or just check if your browser supports it here. Take a look and find your Safari version: this site tells you if the feature is available and, if prefixed, which prefix you'll have to use.

AudioContext feature detection

To be sure you can use the Web Audio API on any browser which supports it, you can use feature detection with relative fallbacks to the vendor-prefixed objects. In case the AudioContext object is not supported, you'll halt the execution of your script and alert the user. Here's an example:

var AudioContext = window.AudioContext // Default
    || window.webkitAudioContext // Safari and old versions of Chrome
    || false; 

if (AudioContext) {
    // Do whatever you want using the Web Audio API
    var ctx = new AudioContext;
    // ...
} else {
    // Web Audio API is not supported
    // Alert the user
    alert("Sorry, but the Web Audio API is not supported by your browser. Please, consider upgrading to the latest version or downloading Google Chrome or Mozilla Firefox");
}

Note that as of now webkit is the only existing vendor-prefixed AudioContext, because Mozilla and Opera use the regular unprefixed object, and IE doesn't support the Web Audio API yet.