(a) Write an equation describing a sinusoidal transverse...

(a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the positive direction of a $y$ axis with an angular wave number of 60 $\mathrm{cm}^{-1}$ , a period of 0.20 $\mathrm{s}$ and an amplitude of 3.0 $\mathrm{mm}$ . Take the transverse direction to be the $z$ direction. (b) What is the maximum transverse speed of a point on the cord?

(a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the positive direction of a $y$ axis with an angular wave number of 60 $\mathrm{cm}^{-1}$ , a period of 0.20 $\mathrm{s}$ and an amplitude
of 3.0 $\mathrm{mm}$ . Take the transverse direction to be the $z$ direction.
(b) What is the maximum transverse speed of a point on the cord?

Key Concepts

Wave Equation

The wave equation is a mathematical formulation that describes how waves propagate through a medium. It incorporates parameters like amplitude, angular frequency, angular wave number, and phase, offering a complete description of the wave’s motion and its propagation direction.

Transverse Motion and Maximum Transverse Speed

In transverse waves, the oscillation of the particles occurs perpendicular to the direction of wave propagation. The maximum transverse speed refers to the highest speed reached by a point on the medium moving up or down during the oscillation, which is directly related to the amplitude and angular frequency of the wave.

Amplitude

The amplitude of a wave represents the maximum displacement of points on the medium from their equilibrium position. It is a measure of the energy carried by the wave and determines the strength of the wave’s effect on the medium.

Sinusoidal Wave

A sinusoidal wave is a type of oscillatory motion that can be described using sine or cosine functions. It represents smooth, repetitive fluctuations in space and time, making it an ideal model for many physical wave phenomena such as vibrations and sound waves.

Angular Wave Number

The angular wave number (often denoted as k) is a measure of the number of wave cycles per unit distance, expressed in radians per unit length. It is inversely related to the wavelength and is a key parameter in defining the spatial characteristics of a wave.

Period

The period of a wave is the duration of time for one complete cycle of the wave to pass a given point. It is inversely related to the frequency and is a fundamental temporal characteristic of the wave.

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