As per Valorum's comment, this is probably Ray Bradbury's "The Murderer".
A psychologist exits the noisy environment to confront a patient confined to a small safe-room. The psychologist notes that its patient has ripped the radio out of the wall to silence it. The room seems unnaturally quiet to the psychologist, yet the patient seems perfectly at ease, even happy. The patient, Albert Brock, calls himself 'The Murderer', and demonstrates his murderous ability by destroying the psychologist's wrist radio.
Questioning reveals that the man had one day been driven mad by the constant expectations of communication inflicted upon him by society- his wife and children could speak with him whenever they wished, wherever they were; any person could call on him, and many did, simply to make use of their communications devices. He gives a striking image of a world in which humans are constantly bombarded by music, advertisement, propaganda and communication. He then describes his revelation; that if he shut off his phone, he could not be bothered by it. When he arrived home on that day, he discovered his wife, frantic at being out of touch with him for so long. This apparently drives home to him their terrible addiction to technology of communication. He begins to destroy things - his phone, his wrist radio, the televisor, any thing that could disrupt the peace he seeks. The man regrets only destroying the Insinkerator, which he used to mangle another piece of equipment. The Insinkerator, a sink drain disposal, he says, was a machine with a good solid purpose which did not disturb him with its functions, did not demand his attention, which only functioned when he asked it to.