Scope, Sequence, and Coordination

A Framework for High School Science Education

Based on the National Science Education Standards

Hooke's Law, Vibrations, Mechanical Waves and Sound

The Wave Model: Water Waves, Seismic waves, Sound and Light

NSES Generalization (p. 180)

Waves, including sound and seismic waves, waves on water, and light waves, have energy and can transfer energy when they interact with matter.

Further Description:

This NSES generalization imposes a wave model on a variety of natural phenomena. The model is successful within limits in most instances mentioned, but fails in other cases. For example, the wave model will not account for the photoelectric effect, this requiring a particle (photon model).

Feynman has successfully accounted for electromagnetic phenomena without any use of the wave model at all (R.P. Feynman, QED: The Strange Theory of Light and Matter, Princeton, N.J.: Princeton University Press, 1985, p. 15):

It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. Iím telling you the way it does behaveClike particles.

The interaction of light with matter requires the introduction of the photon, and this allows development of the quantization of energy. Oscillatory systems exhibit wave properties and are the sources of many different kinds of waves.

Concepts Needed:

Grade 9

Period, wavelength, frequency, amplitude, transverse, longitudinal, water waves

Grade 10

Equilibrium, medium, sound waves, seismic waves, light waves, ray, incidence, reflection, refraction, absorption, diffraction, interference

Grade 11

Resonance, phase, wave speed, intensity, index of refraction

Grade 12

Coherence, standing wave, harmonic motion

Empirical Laws or Observed Relationships:

The speed of sound in a gaseous medium depends upon properties intrinsic to the medium and the temperature of the medium. The speed of seismic waves depends upon the compressibility of the medium, the density of the medium, and whether the waves are transverse or longitudinal. The speed of surface waves on a liquid medium depends upon the compressibility and density of the medium, the depth of the medium, and the wavelength of the waves. The empirical relationship is different for a shallow medium and a deep medium; in the latter case, the dependence of speed on depth vanishes. The most precise value for the speed of all electromagnetic waves, including light waves in vacuum, is 2.99792458 H 108 m/s.

In a medium transparent to the wave, the speed is lower by an amount that depends upon the index of refraction of the medium, which in turn depends upon the frequency of the wave. The speed of a wave is related to the frequency and wavelength by the equation v = fl.

Waves reflect off a boundary between two media at an angle that is equal to the angle of incidence; the incident ray, the normal to the boundary, and the reflected ray lie in the same plane. Reflection, under some circumstances, introduces a 180/ phase shift.

When a light ray encounters a boundary between two transparent media, refraction takes place. The amount of bending of the ray is given by Snell=s law, which relates the angle of incidence, angle of refraction, and the indices of refraction of both media.

The energy of a wave (the intensity of a light wave is its average energy) is proportional to the square of the amplitude. The energy (or intensity) of a wave varies with the inverse square of the distance from a point source. When waves travel through matter, there is always some absorption of the wave energy. The amount of absorption varies widely and depends upon properties of the medium and the frequency of the wave.

When waves from two or more coherent sources arrive simultaneously at the same point in space, the displacements add. Because the various waves may differ in phase, the resulting amplitudes (and therefore intensities) may be either more or less than the arithmetic sum of the individual amplitudes, a phenomenon known as interference.

When a source of waves moves toward an observer, the observed wavelength is shorter than the emitted wavelength; also, when receding from the observer, the wavelength is longer. This is called the Doppler effect.

Theories or Models:

Waves in a material medium result from oscillations of particles of the medium. These disturbances propagate outward because every particle is linked elastically to its neighbors. Electromagnetic waves travel through a vacuum. What oscillates are electric and magnetic fields, and their propagation is governed by laws known as Maxwell=s equations. These equations predict that the speed of electromagnetic waves in vacuum is determined by two constants, one that appears in Coulomb=s law for electric force and another that appears in an analogous inverse square law for magnetism. This predicted speed for electromagnetic waves from the Maxwell theory matches the speed of light. Therefore, for this and other reasons we conclude that light is an electromagnetic phenomenon.

Several of the empirical laws describing electromagnetic waves, including the laws of reflection and refraction, can be derived from Maxwell=s equations.

For specific wavelengths, resonance occurs on violin strings, in organ pipes, and on other structures with boundaries.

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Micro-Unit Description:

Hooke's Law, Vibrations, Mechanical Waves and Sound
Use a graph of force vs. extension of a spring students should be able to find the slope and relate it to the spring "constant" k, observing that different slopes represent springs of different stiffness. (b) Students should observe and develop the concept of standing waves and observe the resonance of sound waves caused by vibrating strings and air columns.

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