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4 m/s. D [cm] 5 Figure 1: What is the wavelength and amplituc numerical values)? Calculate the period of the wave. Express the displacement D as a funct t+p). What is the appropriate sign dians? That is the vertical displacement of t hat is the velocity of the string at a

4 m/s. D [cm] 5 Figure 1: What is the wavelength and amplituc numerical values)? Calculate the period of the wave. Express the displacement D as a funct t+p). What is the appropriate sign dians? That is the vertical displacement of t hat is the velocity of the string at a

College Physics
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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**Wave Analysis and Calculations** The image depicts a graph and accompanying questions related to a sinusoidal transverse wave on a string. Below is a detailed transcription and explanation for an educational context. --- ### Graph Description **Figure 1: Snapshot at t = 0 s** - **Axes:** - Horizontal axis (x): Labeled "x [m]", ranging from 0 to 20 meters. - Vertical axis (y): Labeled "D [cm]", ranging from -4 cm to 4 cm. - **Wave Pattern:** - The graph shows a sinusoidal wave pattern with peaks and troughs indicating its periodic nature. The wave completes roughly one full cycle within the displayed graph. ### Accompanying Questions 1. **Wavelength and Amplitude:** - Determine the numerical wavelengths and amplitude from the graph, marking these values clearly. 2. **Period of the Wave:** - Calculate the period of the wave using relevant wave equations. 3. **Displacement Expression:** - Express the displacement \( D \) as a function of position \( x \) and time \( t \) in the form \( D = A \sin(kx \pm \omega t + \psi) \). - Determine the appropriate sign for the \( \omega t \) term. - Identify the phase constant \( \psi \) in radians. 4. **Vertical Displacement:** - Find the vertical displacement of the string at \( x = 18 \text{ m} \) at \( t = 5 \text{ s} \). 5. **Velocity of the String:** - Calculate the velocity of the string at \( x = 18 \text{ m} \) at \( t = 5 \text{ s} \). ### Additional Information - The wave moves indefinitely in both positive and negative x-directions at a speed of 24 m/s. This image and its details are designed to assist students in understanding wave properties such as displacement, wavelength, amplitude, and velocity, providing a basis for further exploration of wave mechanics.
Transcribed Image Text:**Wave Analysis and Calculations** The image depicts a graph and accompanying questions related to a sinusoidal transverse wave on a string. Below is a detailed transcription and explanation for an educational context. --- ### Graph Description **Figure 1: Snapshot at t = 0 s** - **Axes:** - Horizontal axis (x): Labeled "x [m]", ranging from 0 to 20 meters. - Vertical axis (y): Labeled "D [cm]", ranging from -4 cm to 4 cm. - **Wave Pattern:** - The graph shows a sinusoidal wave pattern with peaks and troughs indicating its periodic nature. The wave completes roughly one full cycle within the displayed graph. ### Accompanying Questions 1. **Wavelength and Amplitude:** - Determine the numerical wavelengths and amplitude from the graph, marking these values clearly. 2. **Period of the Wave:** - Calculate the period of the wave using relevant wave equations. 3. **Displacement Expression:** - Express the displacement \( D \) as a function of position \( x \) and time \( t \) in the form \( D = A \sin(kx \pm \omega t + \psi) \). - Determine the appropriate sign for the \( \omega t \) term. - Identify the phase constant \( \psi \) in radians. 4. **Vertical Displacement:** - Find the vertical displacement of the string at \( x = 18 \text{ m} \) at \( t = 5 \text{ s} \). 5. **Velocity of the String:** - Calculate the velocity of the string at \( x = 18 \text{ m} \) at \( t = 5 \text{ s} \). ### Additional Information - The wave moves indefinitely in both positive and negative x-directions at a speed of 24 m/s. This image and its details are designed to assist students in understanding wave properties such as displacement, wavelength, amplitude, and velocity, providing a basis for further exploration of wave mechanics.
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