HPP Activity 56v1
How can you turn a C into a B?
You can now determine the position of an object from the time it takes the echo to return and the
speed of sound. And you have seen how to take that position information and produce a 2D
image of interfaces inside the human body. It is even possible to construct 3D ultrasound images
as well as realtime movies of a fetus or heart valves in action (you just have to construct the 2D
images quickly enough and often enough to capture the motion). While that is quite impressive,
you might ask, “Is there anything else that we can do with ultrasound devices?” Indeed!
Exploration
The title of this activity refers to musical notes, not your grade in physics. The scenario we are
considering is this: one person holds a tuning fork that produces the musical note middle C. This
corresponds to a frequency of 256 [Hz]. Now, without changing tuning fork in any way, what
might this person do so that an observer standing some distance away will hear a note
corresponding to B, just below middle C? This would correspond to a frequency of 242 [Hz].
GE 1.
1. What do you think the person holding the tuning fork should do, so that the
observer will hear a frequency of 242 [HZ] even though the tuning fork
continues to produce a frequency of 256 [Hz]? It is okay to speculate here!
2. Observe the video clip CarDoppler1.mov. Make sure the speakers are
turned on and the sound controller is not muted. Describe what you heard.
Were there any changes in the sound? If so, when did they occur? Be specific!
3. When you drive down the road blowing the car horn (not recommended), do
you hear any change in frequency while you are driving compared to when you
are sitting in your parked car?
4. Based on your observations from the video clip, what does an observer on
the ground hear as the car approaches and then recedes? Does the frequency
remain constant? If not, when was it highest? When was it lowest?
5. Suppose you are driving in a car and approach someone standing on the side
of the road holding a loud air horn. What do you think you would hear as you
pass the loud horn?
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity 56v1
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6. Observe the video clip CarDoppler2.mov. What does the person in the car
experience as they pass the stationary source of sound?
7. Going back to question number 1, what do you think the person holding the
tuning fork should do, so that the observer will hear a frequency of 242 [HZ]
even though the tuning fork continues to produce a frequency of 256 [Hz]?
Be specific!
Let's see if these observations can be understood in terms of the wave picture of sound. Consider
first, the case of stationary observer and moving source of sound. We might imagine a person
standing on the side of a road observing an approaching ambulance, with siren turned on. You
can observe this situation with the computer simulation Doppler Effect, accessible on the web.
GE 2.
Set the man's speed to zero, the ambulance speed to zero, and the siren
frequency to 500 [Hz]. Play the simulation for a few seconds.
1. Measure the wavelength of sound produced by the siren at rest. Describe
how you did this. Remember to be accurate!
2. What do you think will happen to the wavelength of the sound, as
experienced by the observer, once the ambulance starts to move?
3. Now set the ambulance speed to 150 [m/s]. Play the simulation. Stop it
before the ambulance passes the man. What would the wavelength of the
sound be, as measured by the man?
4. Continue playing the simulation so that the ambulance passes the man.
What is the wavelength of the sound, as measured by the observer?
5. The speed of sound depends on the medium, so assuming the air is not
changing as the ambulance travels, the speed of sound will be the same during
the entire time of the simulation. Given this fact, do the observed wavelengths
and frequencies make sense for the man standing on the road? Explain.
Invention
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 56v1
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When the observer is at rest and the source of sound is moving towards the oberver, the observed
frequency f  is
 c 
f  f 
(1)
c  v s 
where

f
f
c
vs
= observed frequency
= source frequency
= speed of sound
= source speed
When the observer is at rest and the source of sound is moving away from the observer, the
observed frequency is
 c 
f  f 

c  v s 
These two results are sometimes combined into a single equation.
(2)
 c 
f  f 
(3)
c v s 
where the negative sign is used when the source is moving towards the observer, and the positive
sign is used when the source is moving away from the observer.

When the source is at rest and the observer is moving towards the source, the observed
frequency is
c  v o 
f  f 

 c 
(4)
where

vo
= speed of observer
When the source is at rest and the observer is moving away from the source, the observed
frequency is
c  v o 
f  f 
(5)
 c 
Equations (4) and (5) can be combined into a single equation.

Activity Guide
 2010 The Humanized Physics Project
HPP Activity 56v1
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c  v o 
(6)
f  f 

 c 
where the positive sign is used when the observer is moving towards the source, and the negative
sign is used when the observer is moving away from the source.
 observer and source are moving the observed frequency can be expressed as
If both
c  v o 
(7)
f  f 

c v s 
where the upper sign is used when the motion of one object is towards the other, and the lower
sign is used when the motion of one object is away from the other. Note: Equation 7 and the
accompanying explanation encompasses all possibilities (equations 1-6) so you need only
 this one rule!
remembe
The phenomenon that an observer hears a different frequency than what is produced by the sound
source is called the Doppler effect. In fact, it works for any wave, not just sound waves. Police
radar and laser guns use the Doppler effect to determine your speed on the highway, astronomers
use it to determine speed, direction, and distance of celestial objects, and doctors use it in
ultrasound imaging.
Application
GE 3.
1. The v's in equations (1) - (7) are all speeds. Can the values of any of the
speeds ever be zero? If so, which ones and under which circumstances?
2. Can the values of the speeds ever be negative? Think very carefully about
your answer and review the conditions for the equations above.
Consider the case of stationary observer and an ambulance moving towards
the observer.
3. What happens to the observed frequency as the ambulance speed
approaches the speed of sound? Use Equation 7 to help you answer this. Show
your work.
4. Will you be able to use equations (1) - (7) if the source speed exceeds the
speed of sound? Explain why or why not.
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 56v1
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5. For the case of a stationary observer and ambulance moving towards the
observer, make a graph of observed frequency as a function of source speed
for several values of source frequency. Excel might be useful here! Paste your
graph in the space below.
6. How fast must the ambulance move for the observer to not hear the siren at
all – even though the ambulance is still near the observer? Again, Equation 7
should be quite helpful!
7. Consider a person holding a tuning fork that produces a frequency
corresponding to middle C. If the observer remains at rest, what must the
person holding the tuning fork do so that the observer hears a B immediately
below middle C? Be quantitative. Show your work!
But how can we use the Doppler effect in ultrasound imaging? That’s the next
topic!
Activity Guide
 2010 The Humanized Physics Project