How to stop 'is typing' function when user sends message

My 'user is typing' function does not remove the 'is typing', when the user hits enter. So even though a user sends the message, the 'is typing' still displays, until the timer runs out.

Any ideas?

This is my code:

client-side

// Detect typing

      function timeoutFunction() {  
        typing = false;
        socket.emit("typing", false);
        socket.emit("notTyping", true)
      }

      $("#msg").keypress(function(e){
        if (e.which !== 13) {
          if (typing === false && $("#msg").is(":focus")) {
          typing = true;
          socket.emit("typing", true);
          } else {
              clearTimeout(timeout);
              timeout = setTimeout(timeoutFunction, 1500);
            }
          }
      });

      socket.on("isTyping", function(data) {  
        if (data.isTyping) {
          if ($("#"+data.person+"").length === 0) {
            socket.emit("checkTypingFunction");
            $("#chat").append("<div id='"+ data.person +"'><span class='grey'>" + data.person + " is typing...</div>");
            timeout = setTimeout(timeoutFunction, 1500);
          }
        } else {
           $("#"+data.person+"").remove();
          }
      });

server-side:

client.on("typing", function(data) {  
    if (typeof people[client.id] !== "undefined")
    socket.sockets.in(client.room).emit("isTyping", {isTyping: data, person: people[client.id].name});
    client.broadcast.to(client.room).emit("isTyping", {isTyping: data, person: people[client.id].name});
console.log("Someone is typing");
});

via JonasSH