---
title: "A sinusoidal sound wave travels through air at a constant speed of \\(340\\text{ m/s}\\). The graph shows the gauge pressure \\(\\Delta P\\) of the air as a function of position \\(x\\) along the path of propagation at time \\(t = 0\\). A second sound wave propagates through the same air medium with a frequency twice that of the first wave. Which of the following correctly pairs the wavelength \\(\\lambda_1\\) of the first wave with the ratio of the wavelength of the second wave to that of the first wave, \\(\\lambda_2 / \\lambda_1\\)?"
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url: "https://nerd-notes.com/ubq/117430/"
date_modified: "2026-08-04T06:52:08+00:00"
---

# A sinusoidal sound wave travels through air at a constant speed of \(340\text{ m/s}\). The graph shows the gauge pressure \(\Delta P\) of the air as a function of position \(x\) along the path of propagation at time \(t = 0\). A second sound wave propagates through the same air medium with a frequency twice that of the first wave. Which of the following correctly pairs the wavelength \(\lambda_1\) of the first wave with the ratio of the wavelength of the second wave to that of the first wave, \(\lambda_2 / \lambda_1\)?

A sinusoidal sound wave travels through air at a constant speed of \(340\text{ m/s}\). The graph shows the gauge pressure \(\Delta P\) of the air as a function of position \(x\) along the path of propagation at time \(t = 0\). A second sound wave propagates through the same air medium with a frequency twice that of the first wave. Which of the following correctly pairs the wavelength \(\lambda_1\) of the first wave with the ratio of the wavelength of the second wave to that of the first wave, \(\lambda_2 / \lambda_1\)?

![A Cartesian coordinate graph showing a sinusoidal curve plotting gauge pressure \(\Delta P\) in pascals on the vertical axis versus position \(x\) in meters on the horizontal axis. The vertical axis ranges from \(-10\text{ Pa}\) to \(10\text{ Pa}\) with gridlines at increments of \(5\text{ Pa}\), labeled at \(-10\), \(-5\), \(0\), \(5\), and \(10\). The horizontal axis ranges from \(0\text{ m}\) to \(1.20\text{ m}\) with tick marks and vertical gridlines spaced every \(0.20\text{ m}\), labeled at \(0.00\), \(0.20\), \(0.40\), \(0.60\), \(0.80\), \(1.00\), and \(1.20\). A smooth sinusoidal curve starts at \((0, 0)\), rises to a peak at \((0.10, 10)\), crosses zero at \((0.20, 0)\), reaches a trough at \((0.30, -10)\), and completes its first cycle at \((0.40, 0)\). The curve continues through two more identical cycles, completing its third cycle at \((1.20, 0)\). The horizontal axis is labeled \(x\text{ (m)}\) and the vertical axis is labeled \(\Delta P\text{ (Pa)}\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826328-KG6nQ1.jpg)

- **A.** \(\lambda_1 = 0.40\text{ m}\) and \(\lambda_2 / \lambda_1 = 0.5\)
- **B.** \(\lambda_1 = 0.40\text{ m}\) and \(\lambda_2 / \lambda_1 = 2.0\)
- **C.** \(\lambda_1 = 1.20\text{ m}\) and \(\lambda_2 / \lambda_1 = 0.5\)
- **D.** \(\lambda_1 = 1.20\text{ m}\) and \(\lambda_2 / \lambda_1 = 2.0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117430/*