Essential idea: When travelling waves meet they can superpose to form standing waves in which energy may not be transferred.

Nature of science: Common reasoning process: From the time of Pythagoras onwards the connections between the formation of standing waves on strings and in pipes have been modelled mathematically and linked to the observations of the oscillating systems. In the case of sound in air and light, the system can be visualized in order to recognize the underlying processes occurring in the standing waves.

Understandings:

• The nature of standing waves Concept USNA water tank Tacoma Narrows movie

Applications and skills:

• Describing the nature and formation of standing waves in terms of superposition

• Distinguishing between standing and travelling waves

• Observing, sketching and interpreting standing wave patterns in strings and pipes

• Solving problems involving the frequency of a harmonic, length of the standing wave and the speed of the wave

Guidance:

• Students will be expected to consider the formation of standing waves from the superposition of no more than two waves

• Boundary conditions for strings are: two fixed boundaries; fixed and free boundary; two free boundaries

• Boundary conditions for pipes are: two closed boundaries; closed and open boundary; two open boundaries

• For standing waves in air, explanations will not be required in terms of pressure nodes and pressure antinodes

• The lowest frequency mode of a standing wave is known as the first harmonic

• The terms fundamental and overtone will not be used in examination questions

International-mindedness:

• The art of music, which has its scientific basis in these ideas, is universal to all cultures, past and present. Many musical instruments rely heavily on the generation and manipulation of standing waves.

Theory of knowledge:

• There are close links between standing waves in strings and Schrodinger’s theory for the probability amplitude of electrons in the atom. Application to superstring theory requires standing wave patterns in 11 dimensions. What is the role of reason and imagination in enabling scientists to visualize scenarios that are beyond our physical capabilities?

Utilization:

• Students studying music should be encouraged to bring their own experiences of this art form to the physics classroom

Aims:

• Aim 3: students are able to both physically observe and qualitatively measure the locations of nodes and antinodes, following the investigative techniques of early scientists and musicians

• Aim 6: experiments could include (but are not limited to): observation of standing wave patterns in physical objects (eg slinky springs); prediction of harmonic locations in an air tube in water; determining the frequency of tuning forks; observing or measuring vibrating violin/guitar strings

• Aim 8: the international dimension of the application of standing waves is important in music