---
title: "A heavy, uniform wire of mass \\(M\\) and length \\(L\\) hangs vertically from a rigid support. A small block of mass \\(m\\) is attached to the bottom end of the wire. A student generates a transverse wave pulse near the bottom of the wire, which travels upward toward the support. Which of the following expressions represents the ratio \\(\\dfrac{v_{\\text{top}}}{v_{\\text{bottom}}}\\) of the pulse speed at the top of the wire to the pulse speed at the bottom of the wire?"
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url: "https://nerd-notes.com/ubq/116659/"
date_modified: "2026-08-04T05:25:28+00:00"
---

# A heavy, uniform wire of mass \(M\) and length \(L\) hangs vertically from a rigid support. A small block of mass \(m\) is attached to the bottom end of the wire. A student generates a transverse wave pulse near the bottom of the wire, which travels upward toward the support. Which of the following expressions represents the ratio \(\dfrac{v_{\text{top}}}{v_{\text{bottom}}}\) of the pulse speed at the top of the wire to the pulse speed at the bottom of the wire?

A heavy, uniform wire of mass \(M\) and length \(L\) hangs vertically from a rigid support. A small block of mass \(m\) is attached to the bottom end of the wire. A student generates a transverse wave pulse near the bottom of the wire, which travels upward toward the support. Which of the following expressions represents the ratio \(\dfrac{v_{\text{top}}}{v_{\text{bottom}}}\) of the pulse speed at the top of the wire to the pulse speed at the bottom of the wire?

![A vertical schematic diagram showing a uniform wire hanging from a horizontal cross-hatched ceiling. The wire has total length L and mass M, depicted as a thick vertical line segment. A small rectangular block labeled with mass m is attached to the bottom end of the wire. A small transverse wave pulse is depicted near the lower section of the wire, with an arrow pointing upward along the wire labeled v. A vertical coordinate axis y is shown to the right, pointing upward with y = 0 at the bottom block and y = L at the ceiling. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785821128-cVlqq6.jpg)

- **A.** \(\dfrac{M + m}{m}\)
- **B.** \(\sqrt{\dfrac{M}{m}}\)
- **C.** \(\sqrt{1 + \dfrac{m}{M}}\)
- **D.** \(\sqrt{1 + \dfrac{M}{m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116659/*