# Why does a container with fluid make different sounds at different fluid levels?

Have you ever noticed that when you are filling a container with fluid. As it approaches the top, it makes a different sound? You can tell by listening when your about to reach the top. Why is this?

• The same principle that causes large organ pipes to have low note and small organ pipes to have a high note. Look up "standing wave" and acoustics.
– DWin
Jan 4, 2014 at 5:57
• This is least concerned with fluid dynamics and more of acoustics. There is an instrument called "Jaltarang" which works on the principle of standing waves as mentioned by @DWin Jan 4, 2014 at 6:00
• Have a look at the different level of water in this glass music making youtube.com/watch?v=ew-7SwLcHBg this too youtube.com/watch?v=XKRj-T4l-e8 Jan 6, 2014 at 10:39
• Wow, I can't believe no one put the right answer on this question in 2 years! For shame. It's a Helmholtz resonator. Doesn't anyone here know physics!? May 5, 2016 at 14:56
• Ok, I see that there is quite a good answer to a duplicate question here: physics.stackexchange.com/questions/44601/… . The asker may not be aware that filling a bottle and blowing on a bottle depend on the same process, but they do. May 5, 2016 at 14:59

It is caused by standing waves in the container. You get, as a result, harmonics. There are overtones occurring for a fixed frequency.

The changing sound is because a water filled container is like the half open model in the picture below. As the water level rises, the length of the tube decreases. This would lead to a change in the frequency of standing waves in the tube, thereby leading to different sounds.

The wavelength of the standing wave is a function of $L$.

$$v= f\lambda \implies f = \frac{v}{\lambda} \implies f = \frac{v}{4L}$$

• What have harmonics and standing waves got to do with this? It's not a tube. May 5, 2016 at 14:45

This is known as Helmholtz resonance. Essentially, the volume of air in the cavity acts as a spring where the spring constant is dependent on the volume of the air, and damping is dependent on the inertia of air in the neck of the bottle or container.

The frequency is:

or:

frequency = speed of sound / 2 pi * sqrt (opening area / cavity volume * length of neck)

Depending on the shape of the cavity and the configuration of the neck, it may resonate at a particular frequency or at a range of frequencies. I.e. the frequency spectrum may have a single sharp peak, less sharp peak, or many peaks. The quality factor, called Q, determines how sharp the frequency peak is and complicated resonators, such as a seashell you hold up to your ear, have a low Q and are more like white noise than a particular tone.