What is the unit of x-axis of a sound signal?
The below signal has a duration of 3 second and sampling frequency 44100. So should i write Time(s) for the unit of x-axis. 


No. In your graph, the X axis seems to be simply the sample number. I mean, it's a bit strange to ask us, considering you generated the graph, but if you benefit from having it spelled out:

In DSP, signals are represented by a sequence of samples. And if you plot these samples, there's no inherent "units" on the X axis. Your signal has been reduced to a sequence of digital numbers, and the fact that there was a sampling rate that implies some period of time between each sample is simply not there in DSP.