Ahmed1029 said:
What exactly is a signal in wave physics? Is any wave considered a signal?
A signal is information. The presence of a single wave is actual information that the 'source' is switched on. The state 'on-off-on-off', with a switch, will transmit/carry useful binary information as with Morse Code etc. The amount of information governs the bandwidth occupied by a signal. It is worth while discussing this in terms of Radio Transmissions although it applies for all non-continuous waves. I find the optical equivalent less approachable - except for optical communications, of course.
If a radio wave is 'modulated', it can carry a signal. With amplitude modulation the ( eg low frequency square wave) modulat
ing signal produces a string of symmetrical 'sidebands' above and below the carrier frequency.
A 'photograph' of the RF waveform will be the same over the whole of a signal path. The speed of the information (group velocity) will be the same as the speed of the carrier wave the relationships between all the components of the RF signal will be the same.
But
if there's any form of dispersion, the various sidebands will lose their original phase relationship; they arrive at different times and the demodulated waveform may be distorted significantly.
This is termed 'Group Delay Distortion' and is usually caused by the various filters are used to restrict the channel width and in the receiver. It shows the difference in Wave and Group transit time (from Δω and Δk across the bandwidth), rather than the absolute transit time (from ω and k) which is often impossible to measure in practice.
But the absolute transmission time is usually of no consequence; it's the variation of transmission time that counts. Your 'perfect' analogue TV pictures are good (enough) at all distances and on all channel frequencies.