Wave Simulation Device (Wendy Banner)

Author Wendy Banner: Paul Revere Middle School, Science & Robotics

Principles

Dynamics of both transverse and
longitudinal waves. Particle motion of waves; parallel or perpendicular to the wave.
The concepts of amplitude and period.
The elements of wave structure; crest, trough and wavelength.
Mathematical principles and relationships in the unit circle of a sine wave.
- radius of the circle equals the amplitude
- one wavelength is one rotation.
- periodicity is seen as a function of rotation speed.
Scientific modeling: a mechanical device can represent an abstraction.

Standards

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. Emphasis is on describing waves with both qualitative and quantitative thinking.
- HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth.Algebraic relationships and describing those relationships qualitatively.
MSETS1-4. Developing and Using Models
- Modeling in 6–8 builds on K–5 experiences and progresses to developing, using, and revising models to describe, test, and predict more abstract phenomena and design systems.
- Develop a model to generate data to test ideas about designed systems, including those representing inputs and outputs
HS-ETS1-4 Systems and System Models
- Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions including energy, matter, and information flows— within and between systems at different scales.

Materials needed :

A stop watch to demonstrate of to have students replicate the concept of period.

Procedure

Transverse wave simulation:

Firmly clasp the disk mounted handle knob on the back of the model, and smoothly revolve the knob in a uniform circle about it's own axis. This will tilt the disk, causing the balls to slide up and down the rods on the front side i a wave pattern.
Increase the size of the circle being described to increase the amplitude.
Rotate the handle more rapidly to increase period.

Longitudinal wave simulation:

First return the knob handle to its center-most position, causing the balls to line up straight in the horizontal rest position.
Pinch-grab the small metal ring bound by several radiating strings on the back of the model. pull the ring in a circular pathway, keeping it close to the surface of the board. This motion will cause the rods to move from side to side in sequence to simulate longitudinal wave, with rarefaction and compression.

Explanation

A wave is a form of energy transfer that involves vibration of a material substance or of an electromagnetic field. The mechanical wave is propagated by particles that vibrate in place but do not move along the length of the wave's pathway.

Particles may be displaced from side to side parallel to the wave path as a longitudinal, or compression wave. Or, the particles of matter may be displaced up and down perpendicular to the pathway of a transverse wave. Waves may move in straight lines or radiate out in concentric circles or spheres.

The dynamics of a wave are based on the concept of oscillations or cycles, as a repeating motion. The principle is illustrated by the relationship between the unit circle of trigonometry and the dimensions of a sine wave. The lower diagram particularly resembles the array of 12 strings on each controlling hub of the wave machine. One full crank equals one wavelength. A wider circling raises amplitude, as does a greater radius on the unit circle.

Questions

1. If the wavelength of a wave is increased, how does the frequency change?

2. Draw a short set of transverse waves and label the crest, trough, amplitude and the

span of one wavelength

3. Explain the meaning of amplitude and give three real life examples of increased

amplitude in different kinds of waves.

4. Describe the mathematical relationship between period and frequency.

Answers

1. The wave length and frequency off a wave have an inverse relationship, so the frequency

will be decreased as the wavelength increases.

3. Amplitude is the distance a particle travels from it's rest position, half way between it's

crest and it's trough. This is related to the energy or intensity of the wave. The height

of an ocean wave, the loudness of a sound wave, or the brightness of a light wave are

three examples.

4. The word frequency means "waves per second" and the word period means" seconds per wavelength". As such they are the inverse of one another. Three waves per second, (frequency) would mean 1/3 seconds per wave,(period)..

Everyday examples of the principles illustrated

Transverse waves :
- Mechanical (travel through a physical medium)
  - Seismic S-waves (, ripples on water, whipping rope or bridge span.
- Non-mechanical: Are not transmitted through matter, but can pass through.
  - Electromagnetic radiation. All spectra, with visible light and wave based communications technologies being foremost.
Longitudinal waves: (all are mechanical)
- Sound waves, seismic P-waves,

Photos

References

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