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PhysicsClassical Physics

Parts of a Wave: Seven Parameters of a Cosine Wave Function

Identify all seven parameters of a cosine wave: amplitude, wave number, angular frequency, speed, initial phase, wavelength, and period.

Question

A traveling wave is described by

y(x,t)=(0.25 m)cos⁡[(0.30 m−1)x−(0.90 s−1)t+π/3].y(x,t)=(0.25\,\mathrm m)\cos[(0.30\,\mathrm{m^{-1}})x-(0.90\,\mathrm{s^{-1}})t+\pi/3].

Determine (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) initial phase shift, (f) wavelength, and (g) period.

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Evidence boundary

This solution follows the cosine function and all seven requested quantities in OpenStax University Physics Volume 1, Chapter 16, Problem 51. Phase is reported in the original cosine convention. Derived values show unrounded calculations and two-significant-figure answers; no measured waveform is inferred.