---
title: "A wave source moves at a constant speed \\(v_s\\) through a stationary medium toward a stationary detector. The speed of the waves relative to the medium is \\(v\\), where \\(v_s < v\\). The source emits waves with a constant period \\(T_0\\) and unshifted wavelength \\(\\lambda_0\\). Which of the following expressions correctly represents the apparent wavelength \\(\\lambda'\\) measured by the detector directly in front of the moving source?"
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url: "https://nerd-notes.com/ubq/117285/"
date_modified: "2026-08-04T06:45:15+00:00"
---

# A wave source moves at a constant speed \(v_s\) through a stationary medium toward a stationary detector. The speed of the waves relative to the medium is \(v\), where \(v_s < v\). The source emits waves with a constant period \(T_0\) and unshifted wavelength \(\lambda_0\). Which of the following expressions correctly represents the apparent wavelength \(\lambda'\) measured by the detector directly in front of the moving source?

A wave source moves at a constant speed \(v_s\) through a stationary medium toward a stationary detector. The speed of the waves relative to the medium is \(v\), where \(v_s < v\). The source emits waves with a constant period \(T_0\) and unshifted wavelength \(\lambda_0\). Which of the following expressions correctly represents the apparent wavelength \(\lambda'\) measured by the detector directly in front of the moving source?

![A horizontal line represents the axis of motion. A circular icon labeled source S moves to the right with a velocity arrow labeled v_s. Three circular wavefronts are shown centered at successively shifted points along the axis, spaced closer together on the right side. A stationary detector icon labeled D is located on the axis to the right of the source. An arrow labeled v points to the right indicating wave propagation speed toward detector D. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785825915-cKzMJD.jpg)

- **A.** \(\lambda_0 \left( \dfrac{v}{v - v_s} \right)\)
- **B.** \(\lambda_0 \left( \dfrac{v + v_s}{v} \right)\)
- **C.** \(\lambda_0 \left( \dfrac{v - v_s}{v} \right)\)
- **D.** \(\lambda_0 \left( \dfrac{v}{v + v_s} \right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117285/*