Wave Speed and the Doppler Effect

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Wave Speed and the Doppler Effect
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Whiteboard Warmup!
A 15-kg block is hung from a 0.5-m long string of
mass 3 g. When the string is plucked, it produces
a wave that is shown at one instant to the
left. What will be the frequency of the
resulting note?
0.5 m
15 kg
3
FT (15 kg)(10 m/s2) 150 N µ M/L ( 0.003
kg)/(2 m) µ 0.0015 kg/m
0.5 m
v 316.2 m/s
v ?f
? 1m
15 kg
f 316.2 Hz
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Whiteboard Reasoning
A sound wave produced by a 300 Hz source travels
at 343 m/s in air at room temperature. How fast
would a sound wave produced by a 150 Hz source
travel in the same room?
The same amount!! The speed of a wave depends
only on the medium.
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The Doppler Effect!
The Doppler Effect is the shift in the observed
frequency of a wave, based on the relative
velocity of the source and the observer.
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This shows a source that is moving to the right
with a constant velocity.
Observer A has a relative velocity away from the
source, and will hear a lower frequency than the
emitted frequency. Observer B has a relative
velocity toward the source, and will hear a
higher frequency than the emitted frequency.
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If the source and the observer are moving closer
relative to one another, the observer will
perceive a higher frequency than is emitted. If
the source and the observer are moving further
away relative to one another, the observer will
perceive a lower frequency than is emitted.
The Doppler Effect only pertains to frequency. A
common misconception is that the Doppler Effect
changes the volume of the perceived sound. This
is not so! The intensity (volume) only depends
on the distance from the source, and is not a
part of the Doppler Effect
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Doppler Whiteboard!
A small vibrating object on the surface of a
ripple tank is the source of waves of frequency
20 Hz and speed 60 cm/s. If the source S is
moving to the right, as shown above, with speed
20 cm/s, at which of the labeled points will the
frequency measured by a stationary observer be
greatest? (A) A (B) B (C) C
(D) D (E) It will be the same at all four
points.
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Doppler Whiteboard!

• In the Doppler effect for sound waves, factors
  that affect the frequency that the observer hears
  include which of the following?
• I. The speed of the source II. The speed
  of the observer III. The loudness of the
  sound
•  
• I only (B) III only (C) I and II only
• (D) II and III only (E) I, II, and III

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Final Doppler Whiteboard!

• A small vibrating object on the surface of a
  ripple tank is the source of waves of frequency
  20 Hz and speed 60 cm/s. If the source S is
  moving to the right, as shown above, with speed
  20 cm/s, what will be heard by observer A?
• A frequency that is lower than 20 Hz and
  decreasing.
• A frequency that is lower than 20 Hz and
  constant.
• A frequency that is lower than 20 Hz and
  increasing.
• A frequency that is exactly 20 Hz and constant.
• Observer A will not hear anything

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Observer A will hear a constant frequency that is
lower than the emitted frequency. Observer C
will hear a constant frequency that is higher
than the emitted frequency.
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Moving at the Speed of the Waves!
In this case, the source actually stays adjacent
to each of its emitted waves, creating a large
build-up wavefronts directly along its motion.
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Supersonic Motion!
The source actually outruns each of its emitted
waves, creating a large cone of built-up
wavefronts known as a sonic boom. In the case of
sound waves, this would be a large high-pressure
area where all of the wavefronts overlap.
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Boundary Reflections and Intensity
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A small vibrating object S moves across the
surface of a ripple tank producing the wave
fronts shown above. The wave fronts move with
speed v. The object is traveling in what
direction and with what speed relative to the
speed of the wave fronts produced?
Direction Speed (A) To the right
Equal to v (B) To the right Less
than v (C) To the right Greater than
v (D) To the left Less than v (E)
To the left Greater than v
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Boundary Reflections
When a wave reflects off of a more dense medium
than the one in which it is traveling, it will
become inverted.
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When a wave reflects off of a less dense medium
than the one in which it is traveling, it will
not become inverted.
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Boundary Reflections and Superposition Unite!!!
A square wave pulse is incident on a fixed
boundary, as shown below. Draw the shape of the
string 2 seconds later.
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2 seconds later
Red Incident wave contribution Blue Reflected
wave contribution
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Net Wave
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(No Transcript)
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One more time!
A square wave pulse is incident on an open
boundary, as shown below. Draw the shape of the
string 2 seconds later.
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2 seconds later
Red Incident wave contribution Blue Reflected
wave contribution
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Net Wave
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(No Transcript)
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The string shown above is fixed at one end, and
loose on the other. The pulse shown above is
incident on the fixed end. How many reflections
will it make before it returns to the state
(position and velocity) shown above?
(A) One (B) Two (C) Three (D) Four (E)
Five
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Dense boundary Inversion
Non-dense boundary No Inversion
Dense boundary Inversion
Non-dense boundary No Inversion
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Sound Intensity (I)
A measure of the loudness of a sound wave. Units
are Watts per square meter (W/m2) The volume
of a sound wave is governed by the amount of
energy that passes through a given area per
second.
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Sound Intensity!
When sound is emitted by a source, it travels
outward in all directions. This is called a
spherical wave.
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BUT, since the sound wave travels outward in all
directions, but has a set amount of total power,
this means that the power of the sound wave is
spread out over a larger and larger sphere as it
gets further away!
You have the power emitted by the source, but
spread out evenly over an ever-expanding sphere
of sound.
Asphere 4pr2
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I a 1/r2
Intensity has an inverse-squared dependence on
distance from the source of the sound. You can
think of it as the sound wave spreading out
over the surface of a sphere.
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The beauty of the inverse-squared relationship is
so great that some guy actually got it tattooed
on his arm.
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What you need to know
Sound intensity is proportional to 1/r2, where r
is the distance to the source of the sound. Any
type of quantity that spreads outward in all
directions (gravitational field, electric field)
will have an inverse-squared relationship. You
must know how to proportionally reason using the
inverse-squared relationship.
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Butter Gun Whiteboard
Albert Pujols connects with a fast ball and sends
it out of the park. A fan in the outfield
bleachers, 140 m away, hears the hit with an
intensity of 2.2 ? 10-6 W/m2. Assuming no
reflected sounds, what is the intensity heard by
the first-base umpire, 90 ft (27.4 m) away from
home plate?
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Solution
I a 1/r2
Since the umpire is (27.4 m)/(140 m) 0.2 times
the distance from the source of the sound, he
will hear an intensity that is 1/(0.22) 25
times as large!
2.2 ? 10-6 W/m2 25 5.5 ? 10-5 W/m2
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Inverse-Squared Quiz!
At an Occupy Ridgedale Avenue protest, a
loudspeaker is producing sound waves that spread
out in all directions. Protestor A is 5 meters
from the loudspeaker, and receives sound of
intensity 2.5 10-3 W/m2. Protestor B is 10
meters from the loudspeaker. What sound intensity
does she receive?
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r is multiplied by 2
I is multiplied by 1/(22) 1/4
Therefore, I (1/4)(2.5 10-3 W/m2) 6.25
10-4 W/m2