Vernier Software & Technology

# Doppler Effect: Surface Water Waves

## Introduction

Have you ever noticed that when a train or car moves past you rapidly its whistle or horn seems to change to a lower note? In 1842 an Austrian Physicist, Hans Christian Doppler, asserted that sound waves emitted by a moving train would have a higher frequency when moving toward a listener and a lower frequency when moving away. For surface waves in water, Doppler predicted the same type of frequency shift. In particular, a decrease in the frequency of waves propagating behind a source that moves away at a speed vs can be predicted using the Doppler equation

${f_{\text{B}}} = {f_0}\frac{{{v_{\text{w}}}}} {{{v_{\text{w}}} + {v_{\text{s}}}}}$

where vw is the speed of wave propagation in water and f0 is the frequency of the waves created by a stationary source. Doppler also predicted that the frequency increase in front of a source is given by

${f_{\text{F}}} = {f_0}\frac{{{v_{\text{w}}}}} {{{v_{\text{w}}} - {v_{\text{s}}}}}$

## Objectives

In this activity, you will

• Verify the Doppler Equations for surface waves in water by using Logger Pro to analyze two high speed movies.

## Software for Experiment

This experiment uses Logger Pro software for video analysis. The video for analysis is included with the lab book.

## Physics with Video Analysis

See other experiments from the lab book.

 1 Rolling Ball 2 Big and Small: How to Scale an Image 3 Velocity Change 4 Velocity and Speed 5 Velocity and Acceleration 6 Three Movies: Determining Constant Acceleration 7 Demon Drop: A Mathematical Modeling Activity 8 Jumping on the Moon 9 2D Vectors: Pool Ball Displacement, Velocity, and Speed 10 Galileo's Projectile I: Using 17th Century Techniques 11 Galileo's Projectile II: Using Contemporary Techniques 12 Projectile Motion Vectors 13 Frictional Slowing 14 Impulsive Juggling 15 Center of Mass Motions 16 Finding a Spring Constant 17 Net Work - Kinetic Energy Theorem 18 Oscillations 19 Slinky Wave Speeds 20 Superposition of Slinky Waves 21 A Wave Pulse Equation 22 Doppler Effect: Surface Water Waves 23 Doppler Effect: Sound Waves 24 A Heat Engine: Relating Work to the P-V Cycle 25 Coulomb's Law for Two Charged Spheres 26 Discharge Rate 27 Electric Field Due to a Line of Charge 28 Resistance and Ohm's Law 29 Parallel Plate Capacitor: Potential Difference vs. Spacing 30 Wiring Capacitors in Series and Parallel 31 Using RC Decay to Determine Capacitance 32 Exploring Faraday's Law 33 Snell's Law of Refraction

### Experiment 22 from Physics with Video Analysis Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.