According to https://stackoverflow.com/a/23395136/476951 you can make JavaScript beep. I copied the AudioData from there.
Then I'll attach an EventListener on error
to the document
and I'm set.
Please be aware that you cannot play a sound without the user interacting with the document (i.e. click inside the document or similar interactions). So you cannot beep on errors that occur before the first interaction occurred. This means, the first error I create by calling a non-existent function just after load doesn't play the sound, because there was no interaction with the document before.
window.addEventListener('error', () => beep())
document.getElementById('btn--error').addEventListener('click', () => {document.fshdjfds()})
document.fshdjfds()
function beep() {
var snd = new Audio("data:audio/wav;base64,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");
snd.play();
}
<button id="btn--error">Call a non-existent function!</button>