Unit 1.1 Summary
— An oscillating (or vibrating) object undergoes simple harmonic motion (SHM) if the restoring force is proportional to (the negative of) the displacement F = –kx.
— The maximum displacement from equilibrium is called the amplitude.
— The period, T, is the time required for one complete cycle (back and forth).
— The frequency, f, is the number of cycles per second. f = ^{1}/_{T}
— The period of oscillation for a mass m on the end of a spring is given by
— SHM is sinusoidal, which means that the displacement as a function of time follows a sine curve.
— A simple pendulum of length approximates SHM if its amplitude is small and friction can be ignored. For small amplitudes, its period is given by
— The wavelength of a continuous sinusoidal wave is the distance between two successive crests or any two successive points in phase.
— The frequency is the number of full wavelengths that pass a given point per unit time.
— The amplitude of a wave is the maximum height of a crest, or depth of a trough, relative to the normal (or equilibrium) level.
— The wave speed (how fast a crest moves) is equal to the product of wavelength and frequency. v = fλ
— In a transverse wave, the oscillations are perpendicular to the direction in which the wave travels. An example is a wave on a cord.
— In a longitudinal wave, the oscillations are along (parallel to) the line of travel - sound is an example.
— Waves reflect off objects in their path. When the wave front (of a two- or three-dimensional wave) strikes an object, the angle of reflection is equal to the angle of incidence. This is the law of reflection.
— When a wave strikes a boundary between two materials in which it can travel, part of the wave is reflected and part is transmitted. |