---
title: "A sound wave with frequency \\(f_0\\) and wavelength \\(\\lambda_0\\) travels through warm air where its speed is \\(v_0\\). The wave then crosses a boundary into a region of cold air where its speed decreases to \\(\\dfrac{1}{2}v_0\\). What are the frequency and wavelength of the sound wave in the cold air?"
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url: "https://nerd-notes.com/ubq/116623/"
date_modified: "2026-08-04T05:25:19+00:00"
---

# A sound wave with frequency \(f_0\) and wavelength \(\lambda_0\) travels through warm air where its speed is \(v_0\). The wave then crosses a boundary into a region of cold air where its speed decreases to \(\dfrac{1}{2}v_0\). What are the frequency and wavelength of the sound wave in the cold air?

A sound wave with frequency \(f_0\) and wavelength \(\lambda_0\) travels through warm air where its speed is \(v_0\). The wave then crosses a boundary into a region of cold air where its speed decreases to \(\dfrac{1}{2}v_0\). What are the frequency and wavelength of the sound wave in the cold air?

![A rectangular diagram divided vertically into two regions by a dashed line. The left region is labeled Warm Air with wave speed v_0. Inside the left region, a sinusoidal wave with wavelength \lambda_0 travels to the right toward the boundary, indicated by a horizontal arrow labeled Sound Wave. The right region is labeled Cold Air with wave speed v_0 / 2 and contains no drawn wave. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785821119-c9B0dd.jpg)

- **A.** Frequency: \(\dfrac{1}{2}f_0\); Wavelength: \(\lambda_0\)
- **B.** Frequency: \(f_0\); Wavelength: \(\dfrac{1}{2}\lambda_0\)
- **C.** Frequency: \(f_0\); Wavelength: \(2\lambda_0\)
- **D.** Frequency: \(2f_0\); Wavelength: \(\dfrac{1}{2}\lambda_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116623/*