What does "frequency" mean for various kinds of signals? I've been involved in Signal processing for quiet a time but I'm still so confused of what frequency could possibly is, as it has different meanings in different scenarios, for example,

According to Wikipedia,


  Frequency is the number of occurrences of a repeating event per unit
  time.
  
  Calculating the frequency of a repeating event is accomplished by
  counting the number of times that event occurs within a specific time
  period, then dividing the count by the length of the time period. For
  example, if 71 events occur within 15 seconds the frequency is:




This is the most basic definition of the frequency that everybody knows. But what is the definition of Frequency in case of Digital Images and Sounds ?


  For example, if a newborn baby's heart beats at a frequency of 120
  times a minute, its period (the interval between beats) is half a
  second.


make sense so far.

Now here is the Sine wave of various frequencies,



the bottom waves have higher frequencies than those above. The horizontal axis represents time.

The above signal makes sense to me that it has a frequency but how about a non periodic signals like a human voice, ?

Have a look,


this signal is not repeated on any instance so how one could say what is its frequency and how one could count the number of cycles repeated ?

aforesaid,


  Frequency is the number of occurrences of a repeating event per unit
  time.


How does this statement can be true in case of the frequency of human voice ? because when we speak we do not repeat anything than how the voice can have some frequency ?

and in case of images,


  the rapid change in the color is the part of the High frequency of
  the image


How this can be counted as frequency ?
if the image has all the different pixel values how there could be any frequency ?

I am so curious to know deep in detail about the exact definition of Frequency that holds for everything mentioned above.
The key insight that Fourier had when he developed Fourier analysis is that any absolutely integrable (thanks Jason R) function can be represented as the weighted sum of sines and cosines.  Explaining why this is true is way beyond the scope of this answer.  I suggest you study Fourier theory to understand this better.