1. Created by Joshua Toebbe NOHS 2015
SOUND
The Doppler Effect
Created by Joshua Toebbe NOHS 2015

2. Created by Joshua Toebbe NOHS 2015
We know that sound travels at a specific speed in particular mediums.
For air that speed is approximately 340 m/s, depending on temperature and humidity.
This information can be very useful.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

3. Created by Joshua Toebbe NOHS 2015
What are some things that require knowing the speed of sound?
Ultrasound Imaging
Sonic Motion Detectors
Sonar (passive and active)
And of course: using them in a space probe on an unknown planet to determine the atmospheric density and composition. Which is probably the most realistic (insert sarcasm) use of all.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

4. Created by Joshua Toebbe NOHS 2015
We also know that the speed of sound changes depending on the medium.
But there are other ways that it can change as well.
The simplest way is if the source of the sound is moving.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

5. Created by Joshua Toebbe NOHS 2015
For example: A siren on a police car emits a tone which moves at 340 m/s, but if the police car is moving forward at 38 m/s, then their speeds have to be added together.
To a person in front of the police car, the sound is approaching at 378 m/s.
To a person behind the police car the sound is approaching at 302 m/s.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

6. Created by Joshua Toebbe NOHS 2015
At least that’s how you would think it works, but it doesn’t.
You see, the speed of sound doesn’t actually change. It still travels through the air at the same speed.
Instead the wavelength changes.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

7. Created by Joshua Toebbe NOHS 2015
This works because as the car moves forward, each sound wave that gets emitted is farther forward than the previous one.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

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This process smushes (that is a scientific term) the waves closer together in the front of the sound source.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

9. Created by Joshua Toebbe NOHS 2015
Which results in a higher apparent frequency in the front.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

10. Created by Joshua Toebbe NOHS 2015
And a lower apparent frequency behind.
Doppler Effect
Created by Joshua Toebbe NOHS 2015

11. Created by Joshua Toebbe NOHS 2015
And thus a change in wavelength.
Doppler Effect λ λ
Created by Joshua Toebbe NOHS 2015

12. Created by Joshua Toebbe NOHS 2015
The end result is a higher pitched sound in front of the car, and a lower pitched sound behind it.
Doppler Effect λ λ
Created by Joshua Toebbe NOHS 2015

13. Created by Joshua Toebbe NOHS 2015
I’m sure we have all experienced the change in pitch as a police car, ambulance, or fire truck passed by. Maybe it was train, or even a loud car.
Doppler Effect λ λ
Created by Joshua Toebbe NOHS 2015

14. Created by Joshua Toebbe NOHS 2015
This change in pitch is known as the Doppler Effect. (change in wavelength based on movement of source)
Doppler Effect λ λ
Created by Joshua Toebbe NOHS 2015

15. Created by Joshua Toebbe NOHS 2015
Since distance is equal to speed multiplied by time: The period of a wave multiplied by the speed of sound will give us the distance covered in one cycle. Otherwise known as the wavelength.
𝝀=𝒗𝑻
Doppler Effect
Created by Joshua Toebbe NOHS 2015

16. Created by Joshua Toebbe NOHS 2015
So the wave length in front, relative to the source, is moving at the speed of sound, minus the speed of the source.
𝝀 ′ =(𝒗− 𝒗 𝒔𝒐𝒖𝒓𝒄𝒆 )𝑻
Doppler Effect
Created by Joshua Toebbe NOHS 2015

17. Created by Joshua Toebbe NOHS 2015
And the wavelength behind the car is travelling at the speed of sound plus the speed of the source.
𝝀 ′ =(𝒗+ 𝒗 𝒔𝒐𝒖𝒓𝒄𝒆 )𝑻
Doppler Effect
Created by Joshua Toebbe NOHS 2015

18. Created by Joshua Toebbe NOHS 2015
Since frequency is given as the speed of sound divided by its wavelength (the wave speed equation): We have a new Doppler Equation.
𝒇 ′ = 𝒗 𝝀′ = 𝒗 (𝒗± 𝒗 𝒔 )𝑻 = 𝒗 𝒗± 𝒗 𝒔 𝒇
If the source is approaching (-)
If the source is departing (+)
Doppler Effect
Created by Joshua Toebbe NOHS 2015

19. Created by Joshua Toebbe NOHS 2015
Example #1:
A source is moving past a sound sensor in air. The frequency detected in front of the source was 2800 cycles per second, and the frequency detected behind the source was 1800 cycles per second. How fast is the object moving?
Doppler Effect
Created by Joshua Toebbe NOHS 2015

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Example #2:
A source is moving past a sound sensor in an unknown medium. The frequency detected in front of the source was 2700 cycles per second, and the frequency detected behind the source was 1300 cycles per second. The object was clocked by a radar gun to be moving at 21 m/s. What is the speed of sound in the medium?
Doppler Effect
Created by Joshua Toebbe NOHS 2015

21. Created by Joshua Toebbe NOHS 2015
Example #3:
If an object is moving in air at a speed of 18 m/s and emitting a tone at a frequency of 1870 cycles per second. What frequency should be detected in front of the car? And behind the car?
Doppler Effect
Created by Joshua Toebbe NOHS 2015

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Example #4:
A stationary sonar system in salt water (v=1530 m/s) emits sound waves at a frequency of 200 cycles per second toward a target. If the sound returns at a frequency of 450 cycles per second, how fast and in what direction is the target moving?
Doppler Effect
Created by Joshua Toebbe NOHS 2015

23. Created by Joshua Toebbe NOHS 2015
Example #5:
A stationary sonar system in salt water (v=1530 m/s) emits sound waves at a frequency of 200 cycles per second toward a target. If the sound returns at a frequency of 167 cycles per second, how fast and in what direction is the target moving?
Doppler Effect
Created by Joshua Toebbe NOHS 2015

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Practice #1:
A stationary sonar system in salt water (v=1530 m/s) emits sound waves at a frequency of 253 cycles per second toward a target. If the sound returns at a frequency of 141 cycles per second, how fast and in what direction is the target moving?
Doppler Effect
Created by Joshua Toebbe NOHS 2015

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Practice #2:
If an object is moving in air at a speed of 13 m/s and emitting a tone at a frequency of 1757 cycles per second. What frequency should be detected in front of the car? And behind the car?
Doppler Effect
Created by Joshua Toebbe NOHS 2015