Integrated SequencePhysics Chemistry Organic Biology

Web Resources

HyperPhysics - Standing Waves

HyperPhysics - Vibrating String

HyperPhysics - Overtones and Harmonics

Monterey Institute - Properties of Standing Waves
Multimedia presentation.

PY105 Notes - Interference of Waves
Clear, basic introduction to wave superposition, interference, and standing waves.

PY105 Notes - The physics of music
Nice illustration of the concepts of standing waves in understanding how various musical instruments work.

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Special points of emphasis


Atomic Theory

Modern Physics

Even the most basic tools for describing waves mathematically are beyond the scope of non-Calculus based Physics 101. Ordinary wave equations require the calculus of partial differential equations. The mathematics underlying the Schroedinger wave equation is even more advanced. The Schroedinger wave equation is an important expression for quantum electrodynamics, which we will discuss in Atomic Theory and Modern Physics. While waves is a topic that is extremely relevant to Atomic Theory, it is easy to become confused and uncomfortable because of the advanced mathematics underpinning the discussion.

Because of the absence of advanced mathematics at the premedical level, the mathematical underpinnings of the discussion of Atomic Theory later, for example, are not going to be advanced enough to fully flesh out Schroedinger wave mechanics. This is not a problem, except that many students have difficulty studying this way, because it does not reconcile with their habit of achieving a satisfying, saturated understanding of the material before considering it mastered.

In my experience this can lead to a big stumbling block to being able to feel comfortable with what premedical students do need to feel comfortable with, such as to describe electron orbitals, or accept the basic consequences of molecular orbital theory.

In summary, in Atomic Theory, you will need to find the boundaries of your sense of 'not getting it', accept where it is coming from, and not be afraid to understand things in an impressionistic, intuitive way. To really fly conceptually in chemistry without learning the advanced mathematics, it is important to have intuitive ways of understanding you can substitute and accept that there are going to be boundaries to the understanding.

For example, standing waves on a stretched string are a useful analogy for understanding the electron orbitals discussed in Atomic Theory and Modern Physics. At its root, the mathematics that leads to the distribution of possible electron wave forms (orbitals), is very similar to the mathematics that leads to the series of standing waves on a stretched string. In Atomic Theory, you learn the quantum electrodynamical description of the atom, which presents electrons as possessing both particle and wave nature. Standing mechanical waves are a useful starting point for understanding the quantum description of electron waves. When you describe the series of possible waves on a stretched string, the harmonic series, you use a series of numbers to describe the possible states (n = 1,2,3, etc.). These numbers are the same kind of numbers as the quantum numbers describing the possible electron standing waves in an atom.

The quantum numbers distinguish solutions to the Schroedinger wave equation for an electron in an atom, its orbitals, just as the series of numbers in our simple standing wave functions for a stretched string correspond to possible solutions for that wave type.

This is the kind of mental work to build an intuitive, conceptual comfort level in Atomic Theory and Modern Physics. You are not pretending to have an advanced understanding. What you are aiming for is a satisfied and satisfactory understanding.

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