Saltwater in a Ringing Glass

Dear Sir. I am a grade 12 physics student. My classmates and I are completing a phyiscs assignment based on the following problem. "Fill a glass with water. place a teaspoon of salt into the water and stir it with a teaspoon. Explain the change in the sound produced by the clicking of the teaspoon against the glass during the dissolving process." We have completed a number of experiments measuring the change in the frequency during the dissolving process and have found that the frequency of the clicking sound decreases as the salt dissolves. Why is this so? Thanks,
- Nadia (age 17)
Australia

Well, as you dissolve the salt, the water gets more dense. The main springiness in the oscillation of a tapped glass (that is, where most of the potential energy is) is in the glass. The glass bends and changes shape, and the water has to follow. The spring constant (related to how much force the glass resists with when deformed) remains the same for the glass but the mass of the water which must move increases as the salt is dissolved. The standard calculation of the frequency of an oscillator composed of a spring with a mass attached gives an angular frequency of sqrt(k/m) where k is a spring constant and m is the mass that moves. (this is, by the way, how to measure an astronaut’s mass in space when a scale woudn’t work).

Tom

(published on 10/22/2007)