A sinusoidal transverse wave traveling in the negative...

A sinusoidal transverse wave traveling in the negative direction of an $x$ axis has an amplitude of $1.00 \mathrm{cm},$ a frequency of $550 \mathrm{Hz},$ and a speed of 330 $\mathrm{m} / \mathrm{s}$ . If the wave equation is of the form $y(x, t)=y_{m} \sin (k x \pm \omega t),$ what are $(a) y_{m},(\mathrm{b}) \omega,(\mathrm{c}) k,$ and $(\mathrm{d})$ the correct choice of sign in front of $\omega ?$

A sinusoidal transverse wave traveling in the negative direction of an $x$ axis has an amplitude of $1.00 \mathrm{cm},$ a frequency of
$550 \mathrm{Hz},$ and a speed of 330 $\mathrm{m} / \mathrm{s}$ . If the wave equation is of the form $y(x, t)=y_{m} \sin (k x \pm \omega t),$ what are $(a) y_{m},(\mathrm{b}) \omega,(\mathrm{c}) k,$ and $(\mathrm{d})$ the
correct choice of sign in front of $\omega ?$

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Key Concepts

Wave Propagation Direction

The direction of propagation affects the form of the wave equation by determining the sign in front of the ?t term. For waves traveling in the negative x-direction, the correct form of the sinusoidal wave equation uses a plus sign (i.e., y(x, t) = y? sin(kx + ?t)) to accurately describe the phase change with respect to time.

Wave Number

The wave number, represented by k, indicates the spatial frequency of the wave. It is defined as k = 2?/?, where ? is the wavelength, and it describes how many oscillations occur per unit distance along the direction of propagation.

Amplitude

Amplitude refers to the maximum displacement of the wave from its equilibrium position. It is a measure of the wave's strength or intensity, and in the context of sinusoidal waves, it is represented by y? in the wave equation.

Angular Frequency

Angular frequency, denoted by ?, quantifies how rapidly the wave oscillates in time. It is directly related to the frequency of the wave through the relationship ? = 2?f, providing a measure of the phase change per unit time.

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