[theThinker (OP)]

From the telegraph equation, it is found that electrical signals travel at fraction of light speed over transmission lines. For copper cables, the speed is about 0.5 c.

Is such speeds experimentally verified. Can someone point to some experiments verifying the speed from the telegraph equations. 

[evan_au]

I find that in telephone wires, the speed of electrical signals is closer to ²/₃c. But definitely less than c.

In my work, I often find "bridged taps" on telephone wires - old telephone wires that have been left in place, even though they are no longer used. This introduces "nulls" in the frequency response of the used wires, where the signal is largely cancelled.

If you want to do an experiment to demonstrate this, you could connect a signal generator to a short-circuited length of wire.
Measure the voltage across the end of the wire attached to the signal generator with a high-impedance device (eg a Digital Voltmeter or Digital Oscilloscope).

You will find that there is a drop in the voltage at certain frequencies.
This is when the reflected signal (partially) cancels the incoming signal. By measuring the physical length of the cable, and the null frequencies, you can measure the speed of light in this wire (different wire types have slightly different velocities, depending on the capacitance and inductance of the particular cable type).

[Bored chemist]

Do you man this sort of thing?
http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/76.18.html

and
https://en.wikipedia.org/wiki/Velocity_factor

[theThinker (OP)]

Do you man this sort of thing?
http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/76.18.html

and
https://en.wikipedia.org/wiki/Velocity_factor

I don't know electric circuit theory and cannot understand the ucsb paper. I'll have a question.It seems in those experiments, there is a permanent closed conducting path throughout the experiment including detecting the reflected wave. What if I have this:

Instead of a usual signal  generator, I use a steady DC source (may be a HV battery). The pulse is a rectangular pulse due to switch-on for a small time dt; the pulse ends when the contact is broken leaving the transmission line open.  So in this experiment the path is closed only for a short interval dt.  We have a means to detect arrival of the pulse. Would the measured speed be the same and would the wave also be reflected back to the battery end of the wires.   

We may use theoretical analysis, but are there practical situations which could be taken to be representative and so could be accepted as experimental evidence.

[Bored chemist]

"Would the measured speed be the same and
would the wave also be reflected back to the battery end of the wires.   "
Yes, and yes.
What you describe is quite similar to this
https://en.wikipedia.org/wiki/Pulse_forming_network#Blumlein_transmission_line
which is used in practice to produce high voltage pulses.

[theThinker (OP)]

"Would the measured speed be the same and
would the wave also be reflected back to the battery end of the wires.   "
Yes, and yes.
What you describe is quite similar to this
https://en.wikipedia.org/wiki/Pulse_forming_network#Blumlein_transmission_line
which is used in practice to produce high voltage pulses.

Thanks.

Your link is pertinent and helpful.