### Resonance, Harmony and Off-Resonance Beats

• Introduction
• Resonance
• Harmony
• Video & Results
• Materials
• Procedure
• Preparation & Notes

In these activities, students will:

1. Create resonance conditions between a tuning fork and a bottle containing water.
2. Match the resonance conditions of two tuning forks with different pitch to one of two bottles containing different volumes of water.
3. Establish a link between the length of the tuning fork, pitch and the height of the water.
4. Create off-resonance beat patterns using a sound generator and the tuning fork/bottle.

Resonance occurs when two oscillators (ex. objects that move back and forth) have matched frequencies. The result of resonance is a boost in the amplitude of one of the oscillators. Imagine a child on a swing being pushed by an adult:

1. Resonance - If the timing (and phase) of the push by the adult (oscillator #1) matches the timing when the child is at the peak of their back swing (oscillator #2), then the two oscillations are in resonance. The net result is that there is a dramatic increase in the amplitude of the swing because energy is transferred from the adult to the swing.

2. Mismatch - If the adult is out of sync with the swinging child then the oscillations of the adult have no effect or could have a dampening effect on the amplitude of the swinging child (oscillator #2). Energy is not transferred and the child will not swing as high.

Objects have natural frequencies at which they vibrate (or oscillate).

The hanging pipes of a wind chime have a natural pitch when tapped. When you blow into an empty drink bottle, there is a natural pitch with characteristic vibrational frequency. If you strike and hold a tuning fork, which has pitch matched to the natural frequency of the bottle or pipe, resonance will occur. For a bottle, it will vibrate at the matched frequency, which can be heard. The vibrational energy of the tuning fork is transferred to a bottle or wind chime pipe or even the string of a piano.

In this activity, students will:

1. Match the resonant frequency of bottle containing water with a tuning fork by listening for the resonance effect.
2. Compare this effect with an identical second bottle containing water at a different height.
3. Find a new tuning fork that resonates with the second bottle.
4. Draw conclusions about resonant frequency and water height.

Harmony in music refers to the simoultaneous use of pitches (tones or notes) or chords that follow rules of Harmony. In their simplest form, these rules suggest that tones with pitches (frequencies) that even multiples will come together to create a new central tone that is pleasing to the ear. These tones would be described as consonant. When simoultaneous tones are not harmonious, they are termed dissonant. The rules of Harmony are complex and can be follow different traditions. However, it is useful to understand that there are underlying mathematical principles that predict what sounds pleasant to the ear in practice.

In science, harmonics, refers to even multiples of frequency (or wavelength) in waves, including sound waves and other kinds of waves. Simoultaneous tones of harmonic frequencies will also sound consonant (musically harmonious).

Video of resonance transfer with the 512 Hz tuning fork.

Materials

• tuning forks at various frequencies. We purchased 8 tuning forks for \$20 from Fisher (via the Amazon website). These tuning forks, which are made by Medivibe, are the not the highest quality but they work fine for this purpose.

• glass bottles We used 13.7 fluid oz Frappucino bottles from Starbuck's coffee. A variety of bottles should work. We chose these bottles because they have a larger opening. Measurements for matching resonant frequencies will be specific to these bottles.

• Computer with FFTscope (Download free PC and Mac versions) or some sound generator equipment

Resonance between tuning forks and glass bottles

There are variety of ways to approach this activity. Students can demonstrate the concept with 2 bottles, each with a line of appropriate height, and 2 tuning forks per station.

1. Select 2 bottles with 2 tuning forks. Fill each bottle water to the line marked on the bottle.
2. Strike one tuning for on a firm but somewhat soft surface (like a shoe) and hold over each bottle, going back and forth. Do you hear resonance with one bottle? Do hear resonance with both?
3. Strike the other tuning fork and do the same. Do you hear resonance with one bottle? Do hear resonance with both?
4. Make some notes about the frequency of the tuning fork, the length of the tuning fork and the height of the water in the bottle. What patterns emerge?

Generate beat patterns with off-resonance tones

1. Select a bottle with matching tuning fork and note the frequency on the fork. We used 512 Hz and 341 Hz, and found them to work well because they were loud when resonating the Starbuck's bottle.
2. Open FFT scope on the computer. In the lower left corner is the sound generator. Select Sine and type in frequency of the tuning fork (341 or 512, for example).
3. Next tap the tuning fork and hold over the bottle to make the sound louder. Listen to the 2 tones from the fork and the computer. If the frequencies on the tuning fork and the sound generator are accurate, you may a hear a resonant boost in sound. If the 2 sounds create a beat when mixed, the frequencies are not matched. Adjust the sound generator until you find the right frequency. (For our 512 Hz tuning fork from MediVibe, we found resonance with the sound generator set to 508.5 Hz. The 341 Hz tuning fork was resonant with 341 Hz generation with FFTscope)
4. Now change the frequency on fftscope to be 2-5 Hz off from the resonant frequency, and re-tap the tuning fork. If you did not hear beats in the sound in the previous step, you should now hear them.

Listening to Harmonics

1. Repeat the steps from above but this time set the FFTscope frequency to be half or double the frequency of the tuning fork. You will be listening to two harmonic tones.

Can you find a dissonant frequency?

Notes & Preparation

• Many bottles should work for this purpose. We could hear resonance effects for all but the 2 longest wavelength tuning forks with the Frappucino bottle. It can take a bit of time to start with a new shape bottle.
• The best resonance energy transfer is with the 512 Hz tuning fork with the water at 8.2 cm.
• The full height of the bottle is approximately 19 cm.
• We found the following heights for the water in the bottle for each frequency tuning fork. These inexpensive Medivibe education tuning forks may not create tones at the listed frequency, but they worked fine (with adjustments) for our activities.
Optimal Height of the Water for Resonance Transfer
Frequency of Fork (Hz) Approximate Note Height of water (cm) Wavelength*(cm) 1/4 Wavelength (cm)
256.0 C -- 130 32
288.0 D -- 116 29
320.0 E 0.0 103 26
341.3 F 2.0 97 24
384.0 G 3.4 87 22
426.7 A 5.4 77 19
480.0 B 6.8 69 17
512.0 C 8.2 65 16

* assuming the speed of sound is 340 m/s