---
title: "Four strings, labeled W, X, Y, and Z, are fixed at both ends and driven by mechanical oscillators such that each string vibrates in a standing wave pattern at the same constant frequency \\(f_0\\). The properties of each string and the harmonic number \\(n\\) of its standing wave are shown in the table below.  | String | Length | Linear Mass Density | Harmonic Number (\\(n\\)) | |—|—|—|—| | W | \\(L_0\\) | \\(4\\mu_0\\) | 2 | | X | \\(2L_0\\) | \\(\\mu_0\\) | 2 | | Y | \\(2L_0\\) | \\(3\\mu_0\\) | 1 | | Z | \\(3L_0\\) | \\(2\\mu_0\\) | 3 |  Which of the following correctly ranks the tensions \\(T_W\\), \\(T_X\\), \\(T_Y\\), and \\(T_Z\\) in the strings?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/123181/"
date_modified: "2026-09-28T11:57:52+00:00"
---

# Four strings, labeled W, X, Y, and Z, are fixed at both ends and driven by mechanical oscillators such that each string vibrates in a standing wave pattern at the same constant frequency \(f_0\). The properties of each string and the harmonic number \(n\) of its standing wave are shown in the table below.

| String | Length | Linear Mass Density | Harmonic Number (\(n\)) |
|—|—|—|—|
| W | \(L_0\) | \(4\mu_0\) | 2 |
| X | \(2L_0\) | \(\mu_0\) | 2 |
| Y | \(2L_0\) | \(3\mu_0\) | 1 |
| Z | \(3L_0\) | \(2\mu_0\) | 3 |

Which of the following correctly ranks the tensions \(T_W\), \(T_X\), \(T_Y\), and \(T_Z\) in the strings?

Four strings, labeled W, X, Y, and Z, are fixed at both ends and driven by mechanical oscillators such that each string vibrates in a standing wave pattern at the same constant frequency \(f_0\). The properties of each string and the harmonic number \(n\) of its standing wave are shown in the table below.

| String | Length | Linear Mass Density | Harmonic Number (\(n\)) |
|---|---|---|---|
| W | \(L_0\) | \(4\mu_0\) | 2 |
| X | \(2L_0\) | \(\mu_0\) | 2 |
| Y | \(2L_0\) | \(3\mu_0\) | 1 |
| Z | \(3L_0\) | \(2\mu_0\) | 3 |

Which of the following correctly ranks the tensions \(T_W\), \(T_X\), \(T_Y\), and \(T_Z\) in the strings?

- **A.** \(T_Z > T_W = T_X > T_Y\)
- **B.** \(T_Y > T_W = T_Z > T_X\)
- **C.** \(T_Y > T_X > T_Z > T_W\)
- **D.** \(T_Y > T_Z > T_W = T_X\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123181/*