Can't access methods on object's prototype

I can create a Cat object and set a method on it's prototype to print out the cat's name.

var log = function(message) {
  var results = $('#result');
  results.append('<p>' + message + '</p>');
};

function Cat(name) {
  this.name = name;
}

Cat.prototype.speak = function() {
  log('My name is ' + this.name);
};

var fluffy = new Cat('Fluffy');
var tiddles = new Cat('Tiddes');

log(fluffy.name);
fluffy.speak();
log(tiddles.name);
tiddles.speak();

<script src="http://ift.tt/1oMJErh"></script>
<div id="result"></div>

However, when I try to set the cat's prototype to an animal, I can't access the speak method:

function Animal(name, sound) {
    this.name = name;
    this.sound = sound;

    this.speak = function() {
        log(sound + '! My name is ' + name);
    };
}

function Cat(name) {
    this.prototype = new Animal(name, 'Meow');
}

var fluffy = new Cat('Fluffy');

fluffy.speak();  // TypeError: undefined is not a function

Why does fluffy not get the speak() method of its prototype?