# Understanding how the amount of water affects frequency emitted by wine glass

I've looked across the internet for an answer to why changing the water level in a wineglass affects the frequency measured when the rim of the glass is rubbed. Here's what I've found so far:

• Adding water to the glass causes the inertia of the glass to increase which causes the frequency of oscillation of the wine glass to decrease, therefore decreasing the frequency at which the air is displaced. This results in a lower-pitched sound.

However, I've seen some people say the standing wave of the air column inside the glass decreases in frequency since the length of it decreases as water is added. As a result, since the oscillations of the air column standing wave are transferred to the wine glass (and to the air), this is what causes the frequency of the sound to decrease. (https://physics.stackexchange.com/a/312048/254292).

I'm not sure which explanation is the primary factor that affects the frequency heard, or if they are in fact related to each other in some way. I'd like to have a single explanation that incorporates both of these concepts.

• "the standing wave of the air column inside the glass decreases in frequency since the length of it decreases" That is just wrong. The frequency is inversely proportional to the length of the air column. That's why a tuba is a lot bigger than a trumpet. But it is irrelevant, because the frequency is controlled by the natural frequency of the glass (plus the water), not the air. – alephzero Feb 17 at 2:17
• @alephzero Thanks for mentioning that, I made a mistake when typing the question. So what you're saying is that explanation relating to the standing wave within the glass doesn't really affect the actual frequency that is heard by the human ear? – Aditya Mehrotra Feb 17 at 2:35

To enlarge upon Alephzero's comments: The wavelength of a sound of frequency ~1 KHz is about ~1 foot. A wavelength of order ~1 inch is about 12kHz which for most most of us old-timers is inaudible. So if one ramps the water level up and down by ~1 inch in a water-filled glass the effect on the glass resonance frequency be small and hard to hear.

The dominant effect is instead the inertial coupling between the glass walls and the mass of water contained within the glass. As the level of water rises in the glass, so does the degree of coupling, and hence the effective mass of the glass increases relative to its stiffness. This decreases the resonant frequency of the glass as a resonator.

• My question is asking for the actual explanation for this phenomenon, not the correlation between water added and change in frequency produced. – Aditya Mehrotra Feb 17 at 6:42
• The dominant effect is the inertial coupling between the glass walls and the mass of water contained within the glass. as the level of water rises in the glass, so does the degree of coupling, and hence the effective mass of the glass increases relative to its stiffness. This decreases the resonant frequency of the glass as a resonator. My answer has been edited to add this. – niels nielsen Feb 17 at 7:26

However, I've seen some people say the standing wave of the air column inside the glass increases in frequency since the length of it decreases as water is added.

According to this logic, the frequency must increase with increasing water level in the glass. Which goes against the observation. Thus it must be wrong.

As a result, since the oscillations of the air column standing wave are transferred to the wine glass (and to the air), this is what causes the frequency of the sound to decrease.

This is wrong. Sound is a mechanical wave that travels through a medium. Thus what you refer to as “transferring” of the wave from air column to air/glass is just the sound propagating. And sound propagation does not affect the frequency. So there is no mechanism for the frequency to decrease with increasing level of water in the glass.

• So the actual standing wave formed inside of the glass is not the mechanism in charge of the changing frequencies? – Aditya Mehrotra Feb 18 at 0:00
• Yes. It is not. The mechanism for the sound generation in this case is the vibration of the glass. – Superfast Jellyfish Feb 18 at 5:32