<audio id="player" src="My Audio.wav"></audio>

<div>
    <a href="#" onclick="document.getElementById('player').play()">Play</a>
</div>

By doing that, the href="#" will link to that exact same page, and when clicked, the onclick event will play the audio.

Just a note, it is not a bad idea to have a couple of different file formats. That will assist in cross-browser compatibilities.

Actually the href attribute is redirecting you to the new page, you can use e.prevenDefault() in the link click event handler to stop this redirection and create a dynamic audio element with this href as source and play it.

This is what you need:

function playItHere(e, link) {
  var audio = document.createElement("audio");
  var src = document.createElement("source");
  src.src = link.href;
  audio.appendChild(src);
  audio.play();
  e.preventDefault();
}

<a href="https://upload.wikimedia.org/wikipedia/en/4/45/ACDC_-_Back_In_Black-sample.ogg" onclick="playItHere(event, this)">Pronunciation of a word</a>

Try this snippet

list.onclick = function(e) {
  e.preventDefault();

  var elm = e.target;
  var audio = document.getElementById('audio');

  var source = document.getElementById('audioSource');
  source.src = elm.getAttribute('data-value');

  audio.load(); //call this to just preload the audio without playing
  audio.play(); //call this to play the song right away
};

<ul style="list-style: none">
  <li>Audio Files
    <ul id="list">
      <li><a href="#" data-value="http://media.w3.org/2010/07/bunny/04-Death_Becomes_Fur.oga">Death_Becomes_Fur.oga</a></li>
      <li><a href="#" data-value="http://media.w3.org/2010/07/bunny/04-Death_Becomes_Fur.mp4">Death_Becomes_Fur.mp4</a></li>
      <li><a href="#" data-value="http://media.w3.org/2010/11/rrs006.oga">rrs006.oga</a></li>
      <li><a href="#" data-value="http://media.w3.org/2010/05/sound/sound_90.mp3">sound_90.mp3</a></li>
    </ul>
  </li>
</ul>

<audio id="audio" controls="controls">
  <source id="audioSource" src=""></source>
  Your browser does not support the audio format.
</audio>

JSFiddle http://jsfiddle.net/jm6ky/2/