Tune your glasses with salt?

My friend, Chris, mentioned an interesting scientific observation. We were stting on his front porch for the bimonthly knitting club. I was working on oboe reeds, and everyone else was mostly playing with the dog, Chloe. Chris had bacon and peanut-butter flavored bubbles that he would blow into the air and the dog would chase them. He related a scientific observation he had made earlier.
Chris had been mixing up some salt water in a glass. The spoon occasionally hits the side of the glass, and it makes a ringing sound. At first the pitch of the rining dropped. Then, as the salt dissolved, the pitch of the ringing sound went higher. He said he could tell when it had all dissolved because the pitch stopped going up.
Why does this happen?
The pitch that you hear is a function of resonance inside the glass. Let’s hypothesize that the pitch is due to sound waves going back and forth through the water. The speed of sound in tap water at room temperature is about 1500 meters per second. If we assume that the glass Chris used was about 0.05 meters across, we would expect to have a resonance frequence of about 30000 Hertz.
HUMMM, That is above the normal range of human hearing. I guess that the sound produced by hitting a glass with a spoon is not simply a function of the resonance of the glass. Indeed, if it were, you would expect that an empty glass (one filled with air, in which sound travels at 340.29 meters per second) would have a much lower pitch. In fact, an empty glass has a higher pitch when struck with a spoon.
I believe that what we’re observing is the same phenomena that allows a piano or a string instrument to produce lower pitches on strings of the same (or similar) length to those that produce pitches in higher registers. The low strings are heavier! The relationship shows that frequency (i.e. pitch) is inversely proportional to the density (weight) of the string.
The same rule applies to the ringing of the glass. The water in the glass impedes the motion of the glass in the same way that extra weight impedes the motion of the string. The more water the more weight. Thus the more water weight, the lower the pitch.
I believe the observation that the pitch changes as the salt dissolves is untrue has nothing to do with the salt. While experimenting with salt, water, and a glass just now, I observed that by far the largest change in pitch is due to the shape of the water in the glass when it rings. Stirring the water causes the water to rise up along the sides of the glass, effectively raising the mass of more of the it. This causes the pitch to drop. As you stop stirring as vigorously, the water settles down and the pitch rises. I could not detect any difference in pitch between a glass filled with tap water, and one filled to the same level with salt water.

5 thoughts on “Tune your glasses with salt?

  1. I did think of that. Although my observation needed only to see that in a vortex the shape is concave, whereas Grandpa’s work was more detailed than that!

  2. It’s true the volume of the solution will change slightly due to the salt, but that’s not enough to explain the wide change in pitch when stirring a container. For one thing, the pitch settles back down, and moreover, a cup of water will ring with a different pitch when you stir it even if it has no salt.

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