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title: "A string consists of three segments connected in series under a uniform tension \\(T_T\\): Segment 1 has linear mass density \\(\\mu_1 = \\mu\\), Segment 2 has \\(\\mu_2 = 4\\mu\\), and Segment 3 has \\(\\mu_3 = \\frac{1}{4}\\mu\\). An upright wave pulse with frequency \\(f_0\\) and wavelength \\(\\lambda_0\\) travels to the right in Segment 1 toward Segment 2. Which of the following correctly pairs the orientation of the pulse reflected back into Segment 1 at the boundary between Segment 1 and Segment 2 with the wavelength \\(\\lambda_2\\) of the pulse transmitted into Segment 2?"
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url: "https://nerd-notes.com/ubq/116670/"
date_modified: "2026-08-04T05:25:29+00:00"
---

# A string consists of three segments connected in series under a uniform tension \(T_T\): Segment 1 has linear mass density \(\mu_1 = \mu\), Segment 2 has \(\mu_2 = 4\mu\), and Segment 3 has \(\mu_3 = \frac{1}{4}\mu\). An upright wave pulse with frequency \(f_0\) and wavelength \(\lambda_0\) travels to the right in Segment 1 toward Segment 2. Which of the following correctly pairs the orientation of the pulse reflected back into Segment 1 at the boundary between Segment 1 and Segment 2 with the wavelength \(\lambda_2\) of the pulse transmitted into Segment 2?

A string consists of three segments connected in series under a uniform tension \(T_T\): Segment 1 has linear mass density \(\mu_1 = \mu\), Segment 2 has \(\mu_2 = 4\mu\), and Segment 3 has \(\mu_3 = \frac{1}{4}\mu\). An upright wave pulse with frequency \(f_0\) and wavelength \(\lambda_0\) travels to the right in Segment 1 toward Segment 2. Which of the following correctly pairs the orientation of the pulse reflected back into Segment 1 at the boundary between Segment 1 and Segment 2 with the wavelength \(\lambda_2\) of the pulse transmitted into Segment 2?

![A horizontal composite string stretched tightly between two rigid outer walls under uniform tension. The string consists of three connected sections: Segment 1 on the left is drawn as a thin line labeled \(\mu_1 = \mu\); Segment 2 in the middle is drawn as a noticeably thicker line labeled \(\mu_2 = 4\mu\); Segment 3 on the right is drawn as a very thin line labeled \(\mu_3 = \frac{1}{4}\mu\). On Segment 1, an upright single Gaussian wave pulse is shown traveling to the right toward the boundary with Segment 2. A straight horizontal arrow labeled \(v_0\) is positioned directly above the pulse, pointing rightward. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785821129-jEuy33.jpg)

- **A.** Reflected pulse orientation: Upright | Transmitted wavelength: \(\lambda_2 = 2\lambda_0\)
- **B.** Reflected pulse orientation: Upright | Transmitted wavelength: \(\lambda_2 = \dfrac{1}{2}\lambda_0\)
- **C.** Reflected pulse orientation: Inverted | Transmitted wavelength: \(\lambda_2 = \dfrac{1}{2}\lambda_0\)
- **D.** Reflected pulse orientation: Inverted | Transmitted wavelength: \(\lambda_2 = 2\lambda_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116670/*