**Text Transcription for Educational Website:**Consider the following \( y-x \) graph of a wave's position. At time \( t = 0 \), \( x_0 = 2.0 \, \text{m} \), \( y_0 = 1.6 \, \text{m} \), and \( y_{\text{max}} = 2.0 \, \text{m} \).Using the graph, write the mathematical description of the \( y \)-position \( y(x,t) \) of the wave as a function of position \( x \) and time \( t \) if the period of motion is 8.0 s, and the wave moves to the right (toward the positive \( x \)-direction). Round the phase angle to two significant figures.\[ y(x,t) = \]**Graph Description:**The graph is a sinusoidal wave representing the position \( y \) in meters as a function of the horizontal axis \( x \) in meters. Key features of the graph include:- The wave oscillates between \( +y_{\text{max}} = 2.0 \, \text{m} \) and \( -y_{\text{max}} = -2.0 \, \text{m} \), indicating the amplitude of the wave.- At \( x_0 = 2.0 \, \text{m} \), the wave starts at \( y_0 = 1.6 \, \text{m} \).- The waveform is oriented along the \( x \)-axis, with peaks at \( +y_{\text{max}} \) and troughs at \( -y_{\text{max}} \).- The wave pattern shows a typical sinusoidal shape, consistent with the equation that will be derived.

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Consider the following y-x graph of a wave's position. At time t = 0, xo =2.0 m, yo = 1.6 m, and ymax =2.0 m. y(m) +ymas Using the graph, write the mathematical description of the y- position y (x,t) of the wave as a function of position x and Yo time t if the period of motion is 8.0 s, and the wave moves to the right (toward the positive x-direction). Round the phase angle to two significant figures. r(m) y(x,t) = -Ymax

Consider the following y-x graph of a wave's position. At time t = 0, xo =2.0 m, yo = 1.6 m, and ymax =2.0 m. y(m) +ymas Using the graph, write the mathematical description of the y- position y (x,t) of the wave as a function of position x and Yo time t if the period of motion is 8.0 s, and the wave moves to the right (toward the positive x-direction). Round the phase angle to two significant figures. r(m) y(x,t) = -Ymax

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Stretched string

A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.

Question

**Text Transcription for Educational Website:**

Consider the following \( y-x \) graph of a wave's position. At time \( t = 0 \), \( x_0 = 2.0 \, \text{m} \), \( y_0 = 1.6 \, \text{m} \), and \( y_{\text{max}} = 2.0 \, \text{m} \).

Using the graph, write the mathematical description of the \( y \)-position \( y(x,t) \) of the wave as a function of position \( x \) and time \( t \) if the period of motion is 8.0 s, and the wave moves to the right (toward the positive \( x \)-direction). Round the phase angle to two significant figures.

\[ y(x,t) = \]

**Graph Description:**

The graph is a sinusoidal wave representing the position \( y \) in meters as a function of the horizontal axis \( x \) in meters. Key features of the graph include:

- The wave oscillates between \( +y_{\text{max}} = 2.0 \, \text{m} \) and \( -y_{\text{max}} = -2.0 \, \text{m} \), indicating the amplitude of the wave.
- At \( x_0 = 2.0 \, \text{m} \), the wave starts at \( y_0 = 1.6 \, \text{m} \).
- The waveform is oriented along the \( x \)-axis, with peaks at \( +y_{\text{max}} \) and troughs at \( -y_{\text{max}} \).
- The wave pattern shows a typical sinusoidal shape, consistent with the equation that will be derived.

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