Dancing Seeds and Sound (Hans Ludwig)

Title: Dancing Seeds and Sound

Principle(s) Investigated:

• Sound waves are pressure waves (energy) which needs a medium through which to vibrate.
• Pressure
• Energy dissipation
• Vibratory Nodes
• Waveform model of sound

Standards :

Grade Eight – Physical Sciences

MS-PS4-1 - Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.

MS-PS4-2 - Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials

Materials:

• Sound source (iPhone with free "Theremin" app)
• Speaker + Amplifier (Bass-guitar amp)
• Audio cable from source to speaker (⅛” cable + ¼” adapter)
• Flat, thin, smooth surface (3’ x 4’ whiteboard)
• Sprinkles - small, light things to vibrate (poppy seeds)
• Should contrast well with surface material
• Auditory protection

Materials which help but are not necessary

• Spirit level
• Newton’s Cradle

Procedure:

1. Position the speaker pointing up and connect the sound source.
2. Place the vibrating surface close above, directly on, or connected to the speaker
3. Level the surface (This helps seeds not spill off so quickly)
4. Sprinkle the seeds evenly on the surface
5. Produce a loud sound and watch the sprinkles dance on the surface.

I happen to like simple sounds sustained at a specific pitch, e.g. a sine or square wave at a specific frequency, amplified violin, tuba, recordings of drones (long low tones). This allows the sprinkles to dance and organize themselves according to surface vibration at particular locations. They will coalesce at nodes—places where the surface does not vibrate as much as others. Changing the pitch, timbre, or adding a second pitch will change the location of the nodes, creating different patterns of sprinkles.

While playing a song makes the sprinkles dance just as much; long, sustained, simple tones organize the sprinkles into patterns. This helps students picture sound as pressure traveling through the medium with some location having lower or higher pressure than others.

Student prior knowledge:

• P-waves in earthquakes (slinky movement)
• Newton’s First Law of Motion
• Speed of Sound

Explanation:

The movement of the speaker jostles air in the form of a pressure wave—where air particles nominally stay in the same place; molecules simply move in one direction, bump up against adjacent molecules, move farther backward than where they started, and end up nearly exactly where began. This is different from a fan which actually moves particular molecules through others.

The jostling energy (pressure wave) from the air transmits into and through the solid surface—in the same manner as through air, but at a faster speed due to the surface’s density—where it bumps the sprinkles into the air. This process is not unlike a Newton’s Cradle where moving the first ball causes the middle balls to nominally stay in the same place and the final ball shoots out. The sprinkles leap off the surface and into the air where they succumb to gravity and fall back to the surface.

Pressure waves are oscillations of particle pressure. Particles experiencing a pressure wave are closer together than they were at rest, move farther apart than at rest, then commence resting in the same location. These pressure oscillations are generally represented by a sine wave: high pressure = crest; low pressure = trough. When two waves interact, they either reinforce each other (two crests or two troughs meet) or they cancel each other out (a crest meets a trough).

Patterns left on the surface emerge from pressure waves bouncing through the material and interacting with each other. Because we use long, sustained tones, it is easy to identify crest-crest/trough-trough interaction; that is where the particles dance a lot (shows white). We call places where crest-trough interaction cancels out vibration, “nodes;” these appear dark, where sprinkles coalesce.

Volume corresponds with greater differences between high and low pressure (amplitude). Pitch corresponds with the rate of the waves (frequency). Timbre is the combination of two or more tones where the frequency of the higher pitch is a whole-number multiple of the lower frequency, e.g. one can affect the timbre of a tone (100 Hz) by playing a other tones at multiples of 100 Hz: 200 Hz, 300 Hz, 400 Hz, etc. . .

A tone’s waveform—ours was a sine wave—literally maps the path a speaker makes: x-axis = time (this moves at the speed of sound); y-axis = speaker’s motion back & fourth, in & out (high pressure & low pressure).

When the pitch is really low, the whole board vibrates b/c low pitches require more energy.

Questions & Answers:

1) Given what we know about the speed of sound, why did the higher tone make only a small part of the board vibrate and the lower tone made the whole board shake?

A) Given the speed of sound is relatively constant on earth, higher frequencies require less energy and have shorter waveforms. These short waveforms translate to less of the board is activated by higher pitches. The opposite is true for low pitches.

2) When the pitch slid from one to another, why did moving through certain frequencies make the board vibrate louder, crating patterns immediately while others—sometimes right next to the first pitches—vibrate rather generically?

A) As the pitch slides, it’s waves bounce off different surfaces at different times. These subtle variations of time allow for different combinations of wave interaction (standing waves). Certain combinations happen at certain frequencies and not others. Therefore one pitch may focus the vibration whereas another simply shakes.

3) What kind(s) of pitches require more energy? What is the relationship between volume and total energy?

A) At the same volume, low pitches require more energy. There is an inverse relationship between frequency and energy.

Applications to Everyday Life:

• Car horns tend to be high pitched, making them directional (louder in front), while fog horns in lighthouses tend to be low so they carry well over long distances.
• Bike Mechanics sometimes use pitch as a guide when crafting a wheel with even spoke tension. Evenly tensioned wheels are long-lasting and their spokes, when plucked, will ping at a similar pitch.
• Geologists record how much energy was released in an earthquake by studying the timing, shape, and magnitude of p-waves.
• Geologists also determined the size and density of the earth’s core by measuring p-waves' time and intensity on the other side of the planet after earthquakes.
• Engineers build seawalls to withstand the tallest waves of a storm. The tallest waves occur when waves come together and two (or more) crests combine and break at the same time.

Photographs:

The relation between sound, pressure, and sine waveforms.

Patterns of Sand on black Surface

Sine Waveform indicating trough and crest

Videos: