---
title: "Two wave pulses, each of length \\(2d\\) and propagating at constant speed \\(v\\), travel toward each other along a horizontal string as shown.  At time \\(t = 0\\), the positive pulse extends from \\(x = -4d\\) to \\(x = -2d\\) traveling to the right with its maximum displacement \\(+A\\) at \\(x = -2d\\), and the inverted pulse extends from \\(x = 2d\\) to \\(x = 4d\\) traveling to the left with its minimum displacement \\(-A\\) at \\(x = 2d\\).  Which of the following best describes the qualitative graph of the string displacement \\(y\\) as a function of position \\(x\\) at time \\(t = \\dfrac{3d}{v}\\), when the two pulses occupy the interval \\(-d \\le x \\le d\\)?"
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url: "https://nerd-notes.com/ubq/123232/"
date_modified: "2026-09-28T11:57:59+00:00"
---

# Two wave pulses, each of length \(2d\) and propagating at constant speed \(v\), travel toward each other along a horizontal string as shown.

At time \(t = 0\), the positive pulse extends from \(x = -4d\) to \(x = -2d\) traveling to the right with its maximum displacement \(+A\) at \(x = -2d\), and the inverted pulse extends from \(x = 2d\) to \(x = 4d\) traveling to the left with its minimum displacement \(-A\) at \(x = 2d\).

Which of the following best describes the qualitative graph of the string displacement \(y\) as a function of position \(x\) at time \(t = \dfrac{3d}{v}\), when the two pulses occupy the interval \(-d \le x \le d\)?

Two wave pulses, each of length \(2d\) and propagating at constant speed \(v\), travel toward each other along a horizontal string as shown.

At time \(t = 0\), the positive pulse extends from \(x = -4d\) to \(x = -2d\) traveling to the right with its maximum displacement \(+A\) at \(x = -2d\), and the inverted pulse extends from \(x = 2d\) to \(x = 4d\) traveling to the left with its minimum displacement \(-A\) at \(x = 2d\).

Which of the following best describes the qualitative graph of the string displacement \(y\) as a function of position \(x\) at time \(t = \dfrac{3d}{v}\), when the two pulses occupy the interval \(-d \le x \le d\)?

![A Cartesian coordinate system with a horizontal x-axis and a vertical y-axis. The horizontal axis has tick marks labeled -4d, -2d, 0, 2d, and 4d. The vertical axis has tick marks labeled +A, 0, and -A. In the region from x = -4d to x = -2d, a solid line triangular pulse sits above the axis, rising linearly from 0 at x = -4d to +A at x = -2d, then dropping vertically to the axis at x = -2d. A horizontal rightward arrow above this pulse is labeled v. In the region from x = 2d to x = 4d, a solid line triangular pulse sits below the axis, dropping vertically from 0 to -A at x = 2d, then rising linearly to 0 at x = 4d. A horizontal leftward arrow above this pulse is labeled v. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596679-QNBIor.jpg)

- **A.** A flat horizontal line along the axis with \(y = 0\) for all \(x\)
- **B.** A piecewise graph that is zero outside the interval \(-d \le x \le d\) and forms a symmetric triangle with a maximum displacement of \(+2A\) at \(x = 0\)
- **C.** A piecewise graph that is zero outside the interval \(-d \le x \le d\) and consists of a single linear segment with positive slope from \(y = -A\) at \(x = -d\) to \(y = +A\) at \(x = +d\)
- **D.** A piecewise graph that is zero outside the interval \(-d \le x \le d\) and consists of a single linear segment with negative slope from \(y = +A\) at \(x = -d\) to \(y = -A\) at \(x = +d\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123232/*