Increasing tone while mixing sugar in water

[billr]

TL;DR Summary

Tone increases while mixing sugar into water -

I make Hummingbird feed by mixing 1/4 cup granulated sugar into 1 cup of water. I use a small glass pyrex measuring cup with one cup of water measured. It's heated for 1 minute in a microwave and 1/4 cup of sugar is added (no red dye!). I then vigorously stir the sugar and water using a metal spoon, clanging the spoon on the inside of the glass cup, making a tone. Over about a minute or two, as I stir, the tone of the clang noticably increases in frequency. Why? Is it the sugar granules growing smaller or a change in the speed of sound in the sugar solution as the sugar dissolves or something else? I wonder if salt might have a similar effect.

Thanks

 

[Baluncore]

Welcome to PF.

My guess is that the speed of sound is higher in the sugar solution.

The dissolving sugar will cool the water. Monitor the tone and the temperature during the process. Once all sugar is dissolved, reheat the solution in the microwave, and see if temperature or sugar concentration changes the tone, stirring unnecessarily as it cools again.

The solid sugar in the cup, also effectively changes the size of the 'bell' that you ring with the spoon.

 

[Dale]

That would be my first thought as well. A good syrup is much more viscous than water. Before the sugar dissolves it will scatter sound, but the water will be less viscous. So scattering will reduce and viscosity will increase as the process goes on.

One other thing it could be is the temperature change. You could try the same process, but without the sugar. If the sound changes just with water then it is probably the temperature

 

[Baluncore]

When I fill a bucket with water from a tap in summer, it sounds somehow different to when I fill it in winter. The note changes as the water level rises, but it is more than that, it has a different character when the water is cold. I suspect that is due to the change in viscosity with temperature of fresh water.

 

[sophiecentaur]

My guess is that the speed of sound is higher in the sugar solution.

That was my initial reaction, too. However, the speed of sound in water would be too high to dominate the frequency of the 'ding'. As far as I can see, the relevant resonance is due to the lateral vibrations in the thin glass cylinder and a bulk effect of the mass of the glass and its stiffness.

The musical wineglass effect is easier to discuss but in that case the stem stiffness would contribute to the resonance perhaps. Here I would expect increasing the mass of water to reduce the frequency and the link seems to agree.

For the cup i think that the situation is more complicated. The relevant quantities are the mass of the glass wall and the height of the column (equivalent of) as it flexes about a circular cross section (there is no stem to produce an audible ping. The water level acts as a 'stop' as in a guitar fret. The Q of that resonator will be much lower so I'd expect a short ping.

IMO there are three stages in the op's experinent. Firstly, the plain water is added, which will produce an initial frequency. Then, as the sugar is added, the volume will increase, the stop moves up and the mass increases and the frequency would drop . But, once the sugar is dissolved, the total volume will return to near the original volume so the frequency would rise again. I cant think how to model this easily but a three stage experiment would be useful.

Then, of course, there is @Dale 's introduction of the damping effect of the syrup. Sounds very relevant but wouldnt that lower the frequency, rather than raise it? I came across a link which discussed the difference in pitch for red and white wine but i forgot to record the link.

A possible improvement could be if there were two measuring cups and one could be used as a reference with just water in it. No need for memory of the pitch.