1. Helmholtz Resonator – Music from a bottle
Picture Area
These resonators are very different from Organ pipes - relatively small bottles can make very low tones.
Turbulence from the air jet excites the air in the neck of the bottle which vibrates in and out.
Adding water to the bottle reduces the volume V and increases the pitch of the tone.
You will need:
Long-neck beer bottles Short-neck beer bottles
Glass jug elongated bottle
Fill the bottles with varying amounts of water. Have 3-4 older (4th or 5th grade students) blow across the mouth of the bottle to produce sound. They will hear a variety of different pitches. Ask them to figure out:
What produces a lower pitch?
Answer: If there is less water, the pitch is lower.
A higher pitch?
Answer: If you add more water, the pitch gets higher.
What is the sound difference among the different bottles?
Answers will vary.
What is happening?
The bottles have a column of air inside on top of the water. This air column is capable of vibrating. The air blown over the top of the instrument is a form of turbulence that sets the inside air inside into vibrational motion. These vibrations result in a sound wave which is audible to students. Of course, the frequency can be modified by altering the length of the air column (adding or removing water) which changes the wavelength and in turn the frequency. A shorter air column means a shorter wavelength and a higher frequency. A longer air column means a longer wavelength, thus lower frequency.
What the students should leave understanding:
The length of the column affects how high or low the sound is.
There is a connection between the bottles and musical instruments.
The high-ness or low-ness of a sound is called its “pitch”. (This is incomplete, but probably what they will understand. They won’t understand that our cochlea translates wave frequencies into electrical impulses that we hear as varying pitches.)
Musical instrument Helmholtz resonator

2. Organ Pipe Resonators – Music from a tube: Boomwackers
Open ended Tube
Closed ended Tube
These resonators are simply tubes or pipes
At an open end the air vibration/oscillation (along the tube) is maximum (Anti Node).
At a closed end the air cannot vibrate/oscillate so there is a node.
This sets up the standing waves that resonate in the tubes.
For a set tube length L the fundamental (what you will mostly hear) wavelengths are:
lopen =2L and lclosed = 4L ,
so lclosed is 2x lopen !
Or the fundamental frequencies are
nopen = c/lopen = c/2L and nclosed = c/4L ,
so nopen is 2x nclosed ,
And the open ended is one octave above (2 x ) the closed ended.
Closed end
nC = 256 Hz -middle C
lC = 340/256 (m/s*s) = 1.3 meters
For Open tube L= 2.6 m
For Closed tube L= 5.2 m !!

3. Organ Pipe Resonators – Music from a tube: Singing Tubes
Open ended Tube
These resonators are simply tubes or pipes
At an open end the air vibration/oscillation (along the tube) is maximum (Anti Node).
At a closed end the air cannot vibrate/oscillate so there is a node.
This sets up the standing waves that resonate in the tubes.
For a set tube length L the fundamental (what you will mostly hear) wavelengths are:
lopen =L/2 and lclosed = L/4 ,
so lclosed is 2x lopen !
Or the fundamental frequencies are
nopen = c/nopen = 2c/L and nclosed = 4c/L ,
so nopen is 2x nopen ,
And the open ended is one octave above (2 x ) the closed ended.
Open tube L=74 cm
l fundamental = 2*74= 1.48 m,
l 1st = 74 cm
f1 = 230 Hz fundamental,
f2 = 460 Hz,
f3 = 690 Hz
f4 = 920 Hz

4. Sympathetic Vibrations
Sympathetic vibrations – one vibrating item can cause another with same natural frequency to vibrate as well. For the wire demo, natural frequency is based on length of wire. The shorter wires have higher natural frequency. Vibrating long wire causes only other long wire to vibrate. Short wire causes only short stick to vibrate.
SYMPATHETIC TUNING FORKS
These tuning forks (286 Hz) are mounted on resonance boxes. The size of the air column in these boxes is so chosen that it will reinforce the same sound that the tuning fork gives. That is, the box acts as a closed organ pipe and the length of the box corresponds approximately to one-quarter of a wave in air of the sound produced by the fork. Place the resonance boxes aligned and with their openings facing each other.
Now strike one fork sharply with the provided rubber hammer. This throws the box to which the fork is attached into strong vibration. The air column will also be set in vibration and all the air immediately around will be set in vibration. This vibration sets the air column in the other box into vibration sympathetically. This air column in the second box causes the tuning fork to vibrate. The second instrument is thus set into vibration by the first instrument. Prove that one fork sets the other into vibration, by striking one fork, let it vibrate for a few seconds and then hold its prongs.
The same sound will still be heard!
The principle of resonance is all around us -- it enables electronic communication but it
also causes mechanical structures to fail (remember the Tacoma Narrows Bridge
collapse). The ME-311 Resonance Demonstrator provides a clear, easy-to-see
demonstration of resonance. The device consists of a horizontal rod to which are affixed
three pairs of spring-steel wires. A brightly colored mass is affixed to the end of each
wire. When any wire is "plucked," its equal-length counterpart of the opposite side of
the device oscillates with large excursions while the other four wires and weights
remain relatively motionless.

5. Tuning Fork Waves
Simple Idea: Placing a vibrating tuning fork in water allows one to see waves created by this vibration.
Complication: The tuning fork vibrates at around 128 Hz. The speed of sound in air is 343 m/s. The wavelength of these waves then are about 2.7 m. In water the speed of sound is about 1500 m/s – which leads to a wavelength of 12 m! However, the wavelength of the standing waves seen in the water are on the order of millimeters to centimeters – something else must going on to account for a wavelength this small!
Water (ocean) waves a incredibly complex and not fully described by an model. However, in general, the velocity of a wave in water depends on wavelength and possibly water depth if the water is shallow enough. Also, however, there are two main types of waves. Gravity waves in the ocean are due mainly to the force of gravity and inertia. But there is also a second type, mainly present for very small wavelengths on the order of centimeters. These are called “capillary waves” and are due primarily to the force of the surface tension of the water. They have the property that, as wavelengths get shorter, their speed increases! This is called anomalous dispersion. It is very different than, for instance, electromagnetic waves traveling in a vacuum, where speed is constant and as wavelength decreases, frequency simply increases.
As amplitude for wave increases, goes from trochoid shape to sharper peaks – these reach a limit and, after this limit, shoot water from peaks. This is source of initial water bubbles when tuning fork is placed in water – the high amplitude brings wave to limit of peak shape.
The principle of resonance is all around us -- it enables electronic communication but it
also causes mechanical structures to fail (remember the Tacoma Narrows Bridge
collapse). The ME-311 Resonance Demonstrator provides a clear, easy-to-see
demonstration of resonance. The device consists of a horizontal rod to which are affixed
three pairs of spring-steel wires. A brightly colored mass is affixed to the end of each
wire. When any wire is "plucked," its equal-length counterpart of the opposite side of
the device oscillates with large excursions while the other four wires and weights
remain relatively motionless.

6. Supplemental Wave Info
Standing Waves
Standing waves:
Node: point that doesn’t move.
Anti-node: point that moves a lot.
Types:
Transverse and Longitudinal
Propagation Speed:
Inversely related to Density
General
String
T = tension
m = mass
L = length