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)
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)
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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.
####](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b2b1966-cbdc-46cc-aafa-333a90f3e9b8%2Fe1750d42-7a1c-4d53-b0da-1aa619bdb8c7%2Flguemap_processed.jpeg&w=3840&q=75)
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
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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