---
title: "A student investigates the properties of sound waves using a rigid, cylindrical tube of length \\( L = 0.60 \\text{ m} \\). The tube is initially open at one end and closed at the other end by a removable cap. A small speaker is placed near the open end. The speaker is connected to a signal generator that produces a pure tone of variable frequency, creating a standing wave of sound inside the tube. The speed of sound in the air inside the tube is \\( v = 340 \\text{ m/s} \\)."
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url: "https://nerd-notes.com/ubq/117703/"
date_modified: "2026-08-04T07:53:32+00:00"
---

# A student investigates the properties of sound waves using a rigid, cylindrical tube of length \( L = 0.60 \text{ m} \). The tube is initially open at one end and closed at the other end by a removable cap. A small speaker is placed near the open end. The speaker is connected to a signal generator that produces a pure tone of variable frequency, creating a standing wave of sound inside the tube. The speed of sound in the air inside the tube is \( v = 340 \text{ m/s} \).

A student investigates the properties of sound waves using a rigid, cylindrical tube of length \( L = 0.60 \text{ m} \). The tube is initially open at one end and closed at the other end by a removable cap. A small speaker is placed near the open end. The speaker is connected to a signal generator that produces a pure tone of variable frequency, creating a standing wave of sound inside the tube. The speed of sound in the air inside the tube is \( v = 340 \text{ m/s} \).

![A horizontal rectangle representing a hollow tube. To the left of the tube's open end is a small rectangular box labeled 'Speaker' with three concentric, dashed curved arcs expanding toward the tube opening, representing sound waves. The right end of the tube is closed with a thick vertical solid line labeled 'Cap'. A horizontal dimension line with arrows at both ends sits below the tube, indicating its length with the label \( L = 0.60 \text{ m} \). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830011-3rDH6v.jpg)

**Part a)** **Sketch** a representation of the displacement standing wave pattern for the fundamental frequency (first harmonic) inside the top tube provided below. **Sketch** a representation of the displacement standing wave pattern for the next possible harmonic inside the bottom tube.

**Part b)** **Calculate** the fundamental frequency of the sound wave in the tube when it is closed at one end.

**Part c)** The student now removes the cap, so the tube is open at both ends. **Indicate** whether the fundamental frequency of the new tube (open at both ends) is greater than, less than, or equal to the fundamental frequency of the original tube (closed at one end). - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer using physical principles and by referencing the shapes of the standing wave patterns in both cases.


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117703/*