The displacement of a wave traveling in the positive x...

The displacement of a wave traveling in the positive $x$ -direction is $y(x, t)=(3.5 \mathrm{cm}) \cos (2.7 x-92 t),$ where $x$ is in $\mathrm{m}$ and $t$ is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wave?

Key Concepts

Wave Displacement Function

This concept refers to the mathematical description of how a wave propagates through space and time. In general, the wave function describes the oscillating displacement of points in a medium, showing periodic behavior with respect to both spatial and temporal coordinates.

Angular Frequency and Frequency

Angular frequency (?) is the rate of change of the phase of a sinusoidal waveform, defined in radians per second, and it relates directly to the frequency (f), which is the number of oscillations per second measured in Hertz. They are connected by the relation ? = 2?f, making it possible to transition between angular and standard frequency measures.

Wave Number and Wavelength

The wave number (k) is a measure of spatial frequency, expressed in radians per unit distance, and describes how many wave cycles occur over a given distance. Wavelength (?) is the distance over which the wave's shape repeats, and it is inversely related to the wave number by the formula k = 2?/?. Together, these concepts help characterize a wave’s spatial properties.

Wave Speed

Wave speed (v) is the rate at which the wave propagates through a medium. It can be determined by the product of the wave’s frequency and its wavelength (v = f?) or by dividing the angular frequency by the wave number (v = ?/k). This concept links the spatial and temporal aspects of wave motion.

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