Let's break down how to draw the snapshot graph \( D(x, t= \text{ s}) \) based on the given wave information: --- # Step-by-step Solution ## 1. Understand the problem - The wave is moving to the right at **1. m/s**. - The wave's *position* at \( x = 2 \text{ m} \). - The *snapshot* graph shows the displacement \( D \) at various times \( t \) at a fixed position \( x = 2 \text{ m} \). - The graph in the figure shows \( D \) vs. \( t \) at \( x=2 \text{ m} \). --- ## 2. Recall the wave motion properties - The wave moves to the right at \( v = 1. \text{ m/s} \). - The wave's shape indicates the displacement as a function of time at a fixed point. - At \( t= \), the wave's shape is given in the graph. --- ## 3. Derive the wave shape at \( t= \) - The graph shows the displacement \( D \) over time \( t \) at \( x=2 \text{ m} \). - The key points from the graph: | \( t \) (s) | \( D \) (cm) | Description | |-------------|--------------|-------------------------------------| | | | Starting point | | 1/3 | +1 cm | First positive peak | | 2/3 | | Returning to equilibrium | | 1 | -1 cm | Negative peak | | 4/3 | | Returning to equilibrium | | 5/3 | +1 cm | Second positive peak | | 2 | | Back to equilibrium | - The wave shows a periodic oscillation with period \( T \approx 2/3 \text{ s} \) (from peaks). --- ## 4. Find the wave's phase at \( t= \) - The displacement at \( t= \) is ****. - The wave's shape at \( t= \) corresponds to the *initial shape* of the wave at that position. --- ## 5. Determine the wave's shape at \( t= \) - Since the wave moves to the right at \( 1. \text{ m/s} \), the wave's shape at \( t= \) is a *shifted version* of the shape observed in the graph. - To find the *initial shape* at \( t= \), we need to understand the wave's *phase* and *displacement* at the initial position. --- ## 6. Constructing the snapshot graph \( D(x, t=) \) - The snapshot at \( t= \) shows the *initial displacement profile* along the \( x \)-axis. - **Key insight:** - The wave moves to the right at \( 1. \text{ m/s} \). - The shape at \( t= \) is a *displacement profile* that, when moved to the right at \( 1. \text{ m/s} \), matches the shape at later times. - Since the wave's shape at \( t= \) is the *initial displacement*, it is a *wave profile* that can be reconstructed by shifting the graph data. --- ## 7. Final step — Sketch the snapshot at \( t= \) - The initial displacement profile \( D(x, ) \) is obtained by translating the wave shape backward in space, given the known wave speed. - The shape is essentially a sinusoidal or similar periodic wave, with peaks and troughs corresponding to the data points. --- # **Final answer:** - The snapshot graph at \( t= \) shows the *initial displacement distribution* along the \( x \)-axis. - It resembles a wave with peaks and troughs aligned with the given data, centered around the initial position of the wave. - You would draw a wave profile with similar shape (peaks at \( D=+1 \text{ cm} \), troughs at \( D=-1 \text{ cm} \)), at \( t= \), along the \( x \)-axis, consistent with the wave moving to the right at 1 m/s. --- **Note:** To precisely draw the shape, use the data points from the graph to sketch the initial displacement profile along the \( x \)-axis, considering the wave's periodicity and amplitude.