Why does sound pitch change when flowing water temp does in pipe?

[EverCurious]

I have always wondered why there is a noticeable change in the sound of water flowing from a pipe when the water temperature changes. When I first turn on the hot water faucet after a long period of being off, there is a steady pitch of sound I hear. I am referring not to the sound of the water crashing into the basin, but the resonance in the faucet. I can tell when the water is warming by what appears to be a drop in the pitch of the sound.

What exactly is happening?

 

[Danger]

Welcome to PF, Evercurious.
I've sort of noticed that, but never really paid attention to it. It might be that the flow rate reduces as the water heater depletes (I know that mine slows down with time). Moreover, though, it might have something to do with the speed of sound in water varying with temperature. I'm sure that someone will show up with a definitive answer before long.

 

[minger]

First guess would be the speed of sound is changing. One can write the speed of sound as:

$$c = \sqrt{\gamma RT}$$
Where $$\gamma$$ is the ratio of specific heats, R is the gas constant, and T is the absolute temperature.

As the speed of the propagating wave increases, the frequency should change according to the wave law:
$$f = \frac{v}{\lambda}$$
Where $$\lambda$$ is the wavelength of the wave (doesn't change?), c is the speed of sound, and f is the frequency. So, an increase in the speed of sound should cause a increase in the frequency?

Does the pitch raise?

 

[Topher925]

The speed of sound of water will remain relatively constant due to water being an incompressible fluid. I believe the change in pitch is due to water vapor forming in the pipes. However, if you look at most piping layouts in a building, the hot water almost always travels upward from the water heater. This means that there has to be a change in pressure from the water heater to the faucet, which is known as head (measured in ft). I'm guessing that based on this as the water travels higher from the water heater there is obviously less pressure head acting on it and that is causing water vapor to form more easily on its way to the faucet. The forming of this water vapor as the water passes by restrictions such as elbows and valves is the high pitch sound that you hear.

This is just an educated hypothesis and hopefully someone will correct me if I'm wrong.

Minger, I believe that equation for the speed of sound only holds true for gases not incompressible fluids.

 

[EverCurious]

First of all...man I love this site. This was my first question and I am impressed.

No matter where I have used hot water from a tap, I have always noticed this phenomenon. So, that seems to eliminate contributions from any specific arrangement of the plumbing or the water heater capacity. I have read in other portions of this site that sound travels at different speeds within materials based on the material's stiffness rather than based on its density.

As the faucet heats from about 70 degF to 110 degF, could the resonant properties of the faucet change? True, a 40 degree change within brass is a small change in a metal to affect its properties, but is a faucet not akin to a musical instrument? If one put a trumpet in the freezer and the same was left in the hot sun, would blowing under the same conditions produce a different tone? I would think so. In this case the instrument (faucet) is not immediately changing in temperature, but the medium passing through it is changing.

 

[Enthalpy]

OK, I didn't observe it seriously by myself...

Water is compressible, this is why it has a sound velocity. Compressibility increases radically with temperature, as it is related (among others) to the free space between molecules, which changes quickly as we're just a few 10°C over melting temperature.

So yes, sound velocity decreases quickly with increasing temperature, and so would a resonant frequency do if related to sound velocity in water. But so many other resonances are possible:

 

[EverCurious]

Thank you Enthalpy. That is a very viable explanation and makes perfect sense to me. I made another observation. The sound effect is more pronounced as the distance between the valves and the exit point of the water from the faucet increases. (The longer the snout...the easier it is to hear). It's always just bugged me exactly what was going on.

Thanks to all.

 

[Topher925]

OK, I didn't observe it seriously by myself...

Water is compressible, this is why it has a sound velocity. Compressibility increases radically with temperature, as it is related (among others) to the free space between molecules, which changes quickly as we're just a few 10°C over melting temperature.

So yes, sound velocity decreases quickly with increasing temperature, and so would a resonant frequency do if related to sound velocity in water. But so many other resonances are possible:

I disagree. Given the temperature and pressure ranges under consideration, changes in density can be considered negligible. Also, sound velocity does not decrease with increasing temperature. Given the temperatures we are considering its the other way around, the speed of sound increases with an increase of temperature.
http://www.engineeringtoolbox.com/sound-speed-water-d_598.html

The temperature differences under consideration (~30C - 75C) only have a sound velocity change of less than 50 m/s. This is only about a 3% increase/decrease in velocity of sound which I do not believe is large enough to account for the broad band in frequencies that can be heard from a faucet.