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A sinusoidal transverse wave is traveling along a string in the negative direction of the x-axis. The figure below shows a plot of the displacement as a function of position at time t = 0; the scale of the y-axis is set by ys = 4.0 cm. The wave speed along the string is v = 12 m/s. y (cm) Ys N 0 20 40 -Ys x (cm)

A sinusoidal transverse wave is traveling along a string in the negative direction of the x-axis. The figure below shows a plot of the displacement as a function of position at time t = 0; the scale of the y-axis is set by ys = 4.0 cm. The wave speed along the string is v = 12 m/s. y (cm) Ys N 0 20 40 -Ys x (cm)

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### Understanding Sinusoidal Transverse Waves A sinusoidal transverse wave is traveling along a string in the negative direction of the x-axis. The figure below illustrates a plot of the displacement as a function of position at time \( t = 0 \). The scale of the y-axis is set by \( y_s = 4.0 \) cm. The wave speed along the string is \( v = 12 \) m/s. ![Plot of Displacement vs. Position](image-url-placeholder) #### Plot Analysis: - **Axes Layout**: - The x-axis represents the position along the string in centimeters (cm). - The y-axis represents the displacement in centimeters (cm) with the scale \( y_s = 4.0 \) cm. - **Wave Nature**: - The plot shows a single cycle of a sinusoidal wave with peaks and troughs. - The wave starts at a positive displacement, reaching a maximum positive peak at \( y_s \) (4.0 cm). - It crosses the x-axis (0 displacement) at two points, then reaches a maximum negative trough at \( -y_s \) (-4.0 cm). - The wave cycle continues to complete one full wavelength. #### Key Points: - **X-axis Range**: The x-axis spans from 0 to 40 cm, indicating the horizontal displacement. - **Wave Displacement**: The crest and trough of the wave alternate between \( y_s \) and \( -y_s \). #### Summary: This sinusoidal wave is characterized by its periodic oscillations along the string, with the displacement alternating between a maximum positive and a maximum negative value, creating a characteristic 'S' shape. The wave travels with a speed of 12 m/s in the negative x-direction. Understanding such wave behavior is crucial in fields ranging from physics to engineering, where wave mechanics play a pivotal role.
Transcribed Image Text:### Understanding Sinusoidal Transverse Waves A sinusoidal transverse wave is traveling along a string in the negative direction of the x-axis. The figure below illustrates a plot of the displacement as a function of position at time \( t = 0 \). The scale of the y-axis is set by \( y_s = 4.0 \) cm. The wave speed along the string is \( v = 12 \) m/s. ![Plot of Displacement vs. Position](image-url-placeholder) #### Plot Analysis: - **Axes Layout**: - The x-axis represents the position along the string in centimeters (cm). - The y-axis represents the displacement in centimeters (cm) with the scale \( y_s = 4.0 \) cm. - **Wave Nature**: - The plot shows a single cycle of a sinusoidal wave with peaks and troughs. - The wave starts at a positive displacement, reaching a maximum positive peak at \( y_s \) (4.0 cm). - It crosses the x-axis (0 displacement) at two points, then reaches a maximum negative trough at \( -y_s \) (-4.0 cm). - The wave cycle continues to complete one full wavelength. #### Key Points: - **X-axis Range**: The x-axis spans from 0 to 40 cm, indicating the horizontal displacement. - **Wave Displacement**: The crest and trough of the wave alternate between \( y_s \) and \( -y_s \). #### Summary: This sinusoidal wave is characterized by its periodic oscillations along the string, with the displacement alternating between a maximum positive and a maximum negative value, creating a characteristic 'S' shape. The wave travels with a speed of 12 m/s in the negative x-direction. Understanding such wave behavior is crucial in fields ranging from physics to engineering, where wave mechanics play a pivotal role.
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