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$### Understanding Wave Pulse Propagation The figure below illustrates a snapshot graph of a wave pulse on a string at time $ t = 0 $ seconds. The pulse is moving to the right with a velocity of 100 cm/s. To understand the wave dynamics, we are asked to sketch the snapshot graphs of the wave pulse at $ t = -0.01 $ seconds and $ t = 0.01 $ seconds. #### Snapshot Graph at $ t = 0 $ seconds ![Wave Pulse at t=0 s](image-link) The wave profile at $ t = 0 $ seconds displays the initial shape of the wave pulse. ##### Description of the Graph: - **Axes**: The horizontal axis represents the position $ x $ in centimeters (cm), and the vertical axis represents the displacement $ y $. - **Wave Shape**: - The wave begins at $ x = 0 $ cm. - The positive peak reaches approximately at $ x = 2 $ cm. - The wave crosses the x-axis at $ x = 4 $ cm. - A negative trough is found between $ x = 4 $ cm and $ x = 6 $ cm. #### Explanation of Wave Propagation: Due to the pulse traveling to the right at 100 cm/s, we can calculate the displacement for other times using the equation: \[ \Delta x = v \cdot \Delta t \] Where: - $ \Delta x $ is the spatial displacement, - $ v $ is the velocity (100 cm/s), - $ \Delta t $ is the time change. ##### For $ t = -0.01 $ seconds: \[ \Delta x = 100 \, \text{cm/s} \cdot (-0.01 \, \text{s}) = -1 \, \text{cm} \] - The wave pulse shifts to the left by 1 cm compared to its position at $ t = 0 $ seconds. ##### For $ t = 0.01 $ seconds: \[ \Delta x = 100 \, \text{cm/s} \cdot 0.01 \, \text{s} = 1 \, \text{cm} \] - The wave pulse shifts to the right by 1 cm compared to its position at $ t = 0 $ seconds. ####$

Transcribed Image Text:### Understanding Wave Pulse Propagation The figure below illustrates a snapshot graph of a wave pulse on a string at time $ t = 0 $ seconds. The pulse is moving to the right with a velocity of 100 cm/s. To understand the wave dynamics, we are asked to sketch the snapshot graphs of the wave pulse at $ t = -0.01 $ seconds and $ t = 0.01 $ seconds. #### Snapshot Graph at $ t = 0 $ seconds ![Wave Pulse at t=0 s](image-link) The wave profile at $ t = 0 $ seconds displays the initial shape of the wave pulse. ##### Description of the Graph: - **Axes**: The horizontal axis represents the position $ x $ in centimeters (cm), and the vertical axis represents the displacement $ y $. - **Wave Shape**: - The wave begins at $ x = 0 $ cm. - The positive peak reaches approximately at $ x = 2 $ cm. - The wave crosses the x-axis at $ x = 4 $ cm. - A negative trough is found between $ x = 4 $ cm and $ x = 6 $ cm. #### Explanation of Wave Propagation: Due to the pulse traveling to the right at 100 cm/s, we can calculate the displacement for other times using the equation: \[ \Delta x = v \cdot \Delta t \] Where: - $ \Delta x $ is the spatial displacement, - $ v $ is the velocity (100 cm/s), - $ \Delta t $ is the time change. ##### For $ t = -0.01 $ seconds: \[ \Delta x = 100 \, \text{cm/s} \cdot (-0.01 \, \text{s}) = -1 \, \text{cm} \] - The wave pulse shifts to the left by 1 cm compared to its position at $ t = 0 $ seconds. ##### For $ t = 0.01 $ seconds: \[ \Delta x = 100 \, \text{cm/s} \cdot 0.01 \, \text{s} = 1 \, \text{cm} \] - The wave pulse shifts to the right by 1 cm compared to its position at $ t = 0 $ seconds. ####

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The figure below shows a snapshot graph at t = 0s of a wave pulse on a string. The pulse is traveling to the right at 100 cm/s. Draw snapshot graphs of the wave pulse at t = -0.01 s and t = 0.01s 2 Atr=0 s 100 cm/s 4 6 x (cm)