Resource Lesson
The Doppler Effect
Printer Friendly Version
The
Doppler Effect
is the apparent change in a wave's frequency resulting from the relative velocity between the source of the waves and the observer. Although the Doppler Effect is generally associated with sound waves, it is applicable to any type of wave. As a rule of thumb, if the distance between the source and the observer decreases, the apparent frequency (called "f prime" or f') is higher than the actual, real frequency of the source.
Case 1: Observer moving.
If the observer is moving but the source is stationary, the apparent frequency change is evidenced directly and can be calculated with the formula:
Δf / f = v / v
_{w}
where
Δf is the apparent change in frequency,
f is the original frequency,
v is the velocity of the observer with respect to the stationary source,
v
_{w}
is the speed of the wave.
To calculate the final frequency the observer records you would use the relationships:
when the observer
approaches
a wave source: f ' = f + Δf --- a higher frequency
when the observer
recedes
from a wave source: f ' = f - Δf --- a lower frequency
Remember that the actual frequency of the source remains unchanged and that this apparent change in frequency is due to the relative velocity between the source and the observer. Also remember that it is the frequency that is manipulated mathematically when the observer is moving either towards or away from the source.
An analogy
. Suppose that you are a parent watching your child play at the beach. If the child stands still in the shallow water, you note that one wave reaches your child's position each second. However, suppose that the child decides to "rush out to meet" the waves. The child will encounter the waves more frequently as he rushes out towards the deeper water. Instead of one wave reaching him each second, he might meet two or three each second. Conversely, if the child "runs away from the waves" back into the shore, instead of one wave reaching him every second, a wave might only reach him once every 1.5 to 2 seconds. The child can change the "apparent frequency" of the oncoming waves through his motions. How much the frequency changes depends on the child's relative speed.
Refer to the following information for the next three questions.
Suppose there is a stationary air raid siren that is emitting a frequency of 880 hz. You may use 340 m/sec as the speed of sound.
If an emergency official (listener/observer) is racing at 34 m/sec to reach his command post then what frequency would he hear as he approaches the siren's source?
What frequency would he hear if he overshot his turn off and continued at his same rate of speed past his command post?
Describe how a graph of apparent frequency vs position would look for this scenario.
Case 2: Source moving.
When the source is moving, the wavelength is the quantity that is directly affected by the relative motion, not the frequency. Our formula becomes:
Δλ / λ = v / v
_{w}
The following diagram shows a source moving towards the right side of the screen at a constant velocity.
As this source moves towards the right, observers located
behind the source
would receive fewer waves per second so they would perceive an apparent frequency that is lower than the source's true frequency.
Notice that the wavelengths are being drawn farther apart. Longer wavelengths "produce" a lower frequency.
As this source moves towards the right, observers located
in front of the source
would receive more waves per second so they would perceive an apparent frequency that is higher than the source's true frequency.
Notice that the wavelengths are being crowded closer together. Shorter wavelengths "produce" a higher frequency.
Before you examine the variables in this equation and work an example, spend some time with this
physlet animation of the Doppler Effect
by Wolfgang Christian at Davidson College. Notice what happens to the separation in the wavelengths as you adjust the speed of the source. Also notice the shape of the bow wave if you choose a relative speed greater than "1" -- that is, a speed greater than the wave speed.
In this formula,
Δλ is the apparent change in wavelength,
λ is the original wavelength when the source is stationary,
v is the velocity of the source with respect to the stationary observer, and
v
_{w}
is the speed of the wave.
In this case, four steps are needed to calculate the apparent frequency.
Determine the original wavelength using
λ = v
_{w }
/ f
Determine the apparent change in wavelength using
Δλ = λ * (v / v
_{w}
)
Determine the new apparent wavelength using
λ' = λ ± Δλ
receding source:
wavelengths drawn apart
λ' = λ + Δλ
approaching source:
wavelengths crowded together
λ' = λ - Δλ
Determine the new apparent frequency using
f ' = v
_{w}
/ λ'
ALERT! The Doppler Effect for the relative motion of a source does NOT yield the same results as for an observer moving at the same rate. You MUST choose the correct formula when solving your problem!
Refer to the following information for the next three questions.
Suppose there is an ambulance emitting a frequency of 880 hz as it rushes to the hospital at 34 m/sec. You may use 340 m/sec as the speed of sound.
What frequency would a bystander hear as the ambulance approaches his location?
What frequency would he hear once the ambulance has passed his location?
Describe how the graph of apparent frequency vs position in this scenario of the source moving at 34 m/sec would differ from the graph in the previous scenario involving the listener moving at 34 m/sec.
Related Documents
Lab:
Labs -
Directions: Constructive and Destructive Interference
Labs -
Doppler Effect: Source Moving
Labs -
Frequency of Vibrating Strings
Labs -
Illuminance by a Light Source
Labs -
Inertial Mass
Labs -
Interference Shading
Labs -
Pipe Music
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Sample Solutions
Labs -
Ripple Tank Student Involvement Sheet
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Speed of a Wave Along a Spring
Labs -
Speed of Sound in Air
Labs -
Speed of Sound in Copper
Labs -
Video: Law of Reflection
Labs -
Video: Law of Reflection Sample Diagram
Resource Lesson:
RL -
Barrier Waves, Bow Waves, and Shock Waves
RL -
Beats: An Example of Interference
RL -
Interference of Waves
RL -
Interference: In-phase Sound Sources
RL -
Introduction to Sound
RL -
Law of Reflection
RL -
Physical Optics - Thin Film Interference
RL -
Resonance in Pipes
RL -
Resonance in Strings
RL -
Ripple Tank Video Guides
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Sound Level Intensity
RL -
Speed of Waves Along a String
RL -
Vibrating Systems - Simple Pendulums
RL -
Vibration Graphs
RL -
Wave Fundamentals
RL -
Waveform vs Vibration Graphs
REV -
Orbitals
Review:
REV -
Chapter 26: Sound
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Sound
REV -
Waves and Sound
REV -
Waves and Sound
Worksheet:
APP -
Echo Chamber
APP -
The Dog-Eared Page
CP -
Light Properties
CP -
Reflection
CP -
Shock Waves
CP -
Sound
CP -
Waves and Vibrations
NT -
Apparent Depth
NT -
Atmospheric Refraction
NT -
Concert
NT -
Light vs Sound Waves
NT -
Shock Cone
NT -
Sound Waves
NT -
Standing Waves
WS -
Beats
WS -
Beats, Doppler, Resonance Pipes, and Sound Intensity
WS -
Counting Vibrations and Calculating Frequency/Period
WS -
Doppler - A Challenge Problem
WS -
Doppler Effect
WS -
Fixed and Free-end Reflections
WS -
Fundamental Wave Terms
WS -
Illuminance 1
WS -
Illuminance 2
WS -
Interference: In-phase Sound Sources
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
More Practice with Resonance in Pipes
WS -
More Practice with the Doppler Practice
WS -
Practice with Resonance in Pipes
WS -
Practice with the Doppler Effect
WS -
Practice: Speed of a Wave Along a String
WS -
Pulse Superposition: Interference
WS -
Ripple Tank Review
WS -
Sound Vocabulary
WS -
Speed of Sound
WS -
Speed of Sound (Honors)
WS -
Standing Wave Patterns #1
WS -
Standing Wave Patterns #2
WS -
Standing Wave Patterns #3
WS -
Standing Wave Patterns #4
WS -
Vibrating Systems - Period and Frequency
WS -
Wave Phenomena Reading Guide
WS -
Wave Pulses
WS -
Waveform and Vibration Graphs #1
WS -
Waveform and Vibration Graphs #2
TB -
25A: Introduction to Waves and Vibrations
TB -
25B: Vibrations and Waves
TB -
25C: Wave Speed
TB -
25D: Interference
TB -
25E: Doppler
TB -
25F: Doppler Effect (continued)
TB -
26B: Speed of Sound
TB -
26C: Resonance
TB -
26D: Beats
TB -
26E: Decibels
TB -
27A: Light Properties
TB -
Decibels and Sound Intensity #1
TB -
Decibels and Sound Intensity #2
TB -
Interference Re-examined
TB -
Refraction Phenomena Reading Questions
TB -
Sound: Mixed Practice
TB -
Waves and Vibrations
PhysicsLAB
Copyright © 1997-2022
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton