The concepts of carrier frequency and beat frequency are related to each other but serve different purposes in the context of waveforms and audio perception.
In the context of modulation, the carrier frequency refers to the high-frequency signal that carries the information of interest. It is modulated by another signal, such as an audio signal, in order to encode that information. The carrier frequency itself does not convey the specific information; rather, it provides the medium for the modulating signal to be transmitted. In radio communication, for example, the carrier frequency is modulated by an audio signal to transmit voice or data.
On the other hand, beat frequency is the difference between two frequencies that are interacting or interfering with each other. When two different frequencies are combined, they create an audible beat or pulsation. This beat frequency is the difference between the two original frequencies. For example, if you have two pure tones of frequencies 500 Hz and 375 Hz, the beat frequency would be 125 Hz (500 Hz - 375 Hz = 125 Hz). This beat frequency is perceived as a pulsation or "beating" sound.
Now, if you want to hear a specific frequency of 125 Hz, known as gamma, you would not use beat frequency for that purpose. Gamma waves refer to a specific range of frequencies associated with brain activity, rather than an audible frequency that you can directly hear. Gamma waves typically fall within the range of 25 to 100 Hz and are not within the typical range of audible frequencies for human hearing.
If you're interested in listening to a pure tone of 125 Hz, you would require a carrier frequency that matches the desired frequency. In this case, the carrier frequency would be 125 Hz itself. By generating a waveform or using an audio device that produces a pure tone of 125 Hz, you would be able to hear that frequency directly without involving beat frequencies.