That would just be graph of y=1/x
I've seen voltage vs. time, voltage vs. frequency but never time vs. frequency

frequency v time is a spectrograph ?

https://en.wikipedia.org/wiki/Spectrogram#:~:text=A common format is a,each point in the image.

 

That would just be graph of y=1/x
I've seen voltage vs. time, voltage vs. frequency but never time vs. frequency

Such a graph might be used to show oscillator drift.

 

I am trying to understand the use of audio frequencies. Frequency is measured in Hertz (Hz), I see that the graph of the signals drawn in one axis shows the frequency and the other shows the time. I don't understand what is the use of measuring signal by frequency.

I see that microphone converts audio signal into voltage signal. The processor takes the voltage signal and processes it. and a display device shows the frequency of the signal. I do not understand why we have to measure the frequency, what are its benefits?

In electronics, frequency is quantity specified in "cycles per second", or "hertz", that represents how often voltage, or current, repeatedly rises and falls. "audio frequency" represents a specific range of frequencies, usually from 20hz to 20,000 hz, the majority of which can be heard by human ears. You'll learn later that audio circuits (like your microphone circuit) will need to be "tuned" to accept, or reject, certain frequencies. You'll need to be able to identify these frequencies, by measuring them, in order to tune the circuit so it can properly amplify the desired "frequencies".

 

The ear is a frequency receptor, not a time receptor.
The ear responds to 1kHz, not 1ms.

The ear/brain system is a time receptor as it can measure time shifts from the same frequency source using our two ears. Our ears are more than just audio transducers, they are Auditory nerve phased-locked (the ear generates sounds) so we can extract timing differences between a sound arriving at each of the two ears, enabling us to localize interaural time differences down to 20us. Relative timing at very short intervals is a natural construct.

 

The ear/brain system is a time receptor as it can measure time shifts from the same frequency source using our two ears. Our ears are more than just audio transducers, they are Auditory nerve phased-locked (the ear generates sounds) so we can extract timing differences between a sound arriving at each of the two ears, enabling us to localize interaural time differences down to 20us. Relative timing at very short intervals is a natural construct.

Is the ear/brain system detecting phase differences or is it amplitude differences?

 

Is the ear/brain system detecting phase differences or is it amplitude differences?

Both and all at the same time. Our hearing can even measure sound reflections phase differences from the direct sound.
https://www.researchgate.net/public...of_Human_Hearing_to_Changes_in_Phase_Spectrum