transverse periodic wave is represented by the equation $y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{s} t-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$. What are the wavenumber $k$ and direction of propagation of the wave?
A) $15.0 \mathrm{~m}^{-1}$; traveling in the $+\mathrm{x}$ direction
B) $30.0 \mathrm{~m}^{-1}$; traveling in the $+\mathrm{y}$ direction
C) $15.0 \mathrm{~m}^{-1}$; traveling in the $-\mathrm{x}$ direction
D) $45.0 \mathrm{~m}^{-1}$; traveling in the $+x$ direction
E) $30.0 \mathrm{~m}^{-1}$; traveling in the $-\mathrm{y}$ direction

Question

Quizplus · Accepted Answer

The wavenumber $k$ is given directly in the wave equation as $15.0 \mathrm{~m}^{-1}$. The wave is traveling in the $+\mathrm{x}$ direction because the argument of the cosine function is of the form $\omega t - kx$, indicating a wave moving in the positive x-direction.

Transverse Periodic Wave Is Represented by the Equation y(x,t)=2.50 cmcos⁡(2,500rad/st−15.0 m−1x)y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{s} t-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)y(x,t)=2.50 cmcos(2,500rad/st−15.0 m−1x)

Transverse Periodic Wave Is Represented by the Equation $y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{s} t-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$