Re: why does the tone produced by water through a tap change?

This is a very interesting question, and despite a multitude of attempts 
at different faucets I have been unable to reproduce the effect you 
discuss.  I do however have some good guesses at what may be behind it.  
Believe it or not this is a complex problem that could have any number of 
possible answers, I will give you my best two guesses and leave it to you 
to prove me right or wrong. 

My first guess is that you are hearing a sort of Doppler effect, similiar 
to that of a train whistle sounding like a higher frequency when traveling 
towards you and a lower frequency when going away from you.  In this case 
however the sound source (flowing water) is moving at a constant speed, 
but the speed of sound in water increases significantly. At 0 degrees C 
the speed of sound in water is 1402 m/s and at 20 degrees C it is 1482 m/s
(the sound is traveling 180 mph faster in the warmer water!). 

My second guess is that the sound you are hearing is not that of the water 
flowing in the pipes but that of the water striking the bottom of the sink.
For this case the important parameter is the viscosity of the water.  More 
viscous materials generally "stick together" better than less viscous 
materials. Cold water has many times the viscosity of warm water.  As it 
exits the faucet therefore the cold water would tend to break into larger 
drops that strike the sink less frequently making a lower tone, while  
warm water would form smaller drops that hit the sink more quickly (making 
a higher tone. 

I hope this helps to answer your question, other possibilities are the 
thermal expansion of the pipes, the turbulent flow of the water that makes 
the noise is modified by the temperature.  The best way to get to the 
bottom of this problem is to find out what is reponsible for the sound you 
are hearing.