A hearing device includes at least one microphone configured to capture sound signals within an overall frequency range and to convert them into an input signal. A signal processor is provided for processing the input signal within a lower frequency range that is part of an overall frequency range. A detector is provided for detecting a noise that has frequency components both inside and outside the lower frequency range, namely in an upper frequency range above the lower frequency range. The hearing device is configured in such a way that the detector detects the noise based on its frequency component in the upper frequency range. A method for operating a hearing device is also provided.