We have a few questions about the Howler that Dumbledore sent Petunia in the rather chaotic kitchen scene at the beginning of Order of the Phoenix. We even have one that asks why Harry didn’t recognise Dumbledore’s voice.
But how is it that Petunia seemingly did recognise Dumbledore’s voice? There’s nothing very identifying, even to Petunia, about the words “Remember my last”. Once she knows the sender is Dumbledore, she would be able to identify that it’s a reference to his last letter to her (when leaving Harry on her doorstep); but the words themselves won’t help her much in identifying who’s speaking.
Moreover, unlike Harry, there is no reason to believe that Petunia had ever heard Dumbledore’s voice before. She’s never been to Hogwarts; his first letter to her was presumably a regular letter; and he never entered the house or spoke to her when he left Harry on her doorstep.
Of course, Dumbledore was likely the only person in the wizarding community that Petunia had ever communicated with (apart from James and Lily), so thinking about it logically, she should be able to work out that it must be from him—but she seems to react immediately and instinctively, rather than spending time turning it logically over in her head:
An awful voice filled the kitchen, echoing in the confined space, issuing from the burning letter on the table.
‘Remember my last, Petunia.’
Aunt Petunia looked as though she might faint. She sank into the chair beside Dudley, her face in her hands.
Order of the Phoenix, ch. 2 “A Peck of Owls”
So how did Petunia immediately recognise Dumbledore’s voice from the Howler?