16.14: Modes d'ondes stationnaires
A closer look at earthquakes provides evidence for conditions appropriate for resonance, standing waves, and constructive and destructive interference. During an earthquake, a building may vibrate for several seconds with a driving frequency matching that of the natural frequency of vibration of the building—producing a resonance that results in one building collapsing while neighboring buildings do not. Similarly, often buildings of a certain height are devastated, while other taller buildings remain intact, occurring because the height of a taller building can create a standing wave with the earthquake waves. In addition, as the earthquake waves travel along the surface of the Earth and reflect off denser rocks, constructive interference occurs at certain points. Often areas closer to the epicenter are not damaged, while areas farther away are damaged.
Meanwhile, standing waves on strings have a frequency that is related to the propagation speed of the disturbance on the string. The wavelength is determined by the distance between the points where the string is fixed in place. The symmetrical boundary conditions (a node at each end) dictate the possible frequencies that can excite standing waves. Starting from a frequency of zero and slowly increasing, the first mode n = 1 appears. The first mode, also called the fundamental mode or the first harmonic, has half of a wavelength, so the wavelength is equal to twice the length between the nodes.
This text is adapted from Openstax, College Physics, Section 16:10: Superposition and Interference, Openstax, University Physics Volume 1, Section 16.5: Interference of Waves, and Openstax, Physics Volume Volume 1, Section 16.6: Standing Waves and Resonance.
