today’s topic the doppler effect - verona public schools · today’s topic: the doppler effect...
TRANSCRIPT
Today’s Topic:
The Doppler Effect
Learning Goal:
SWBAT explain what the Doppler Effect is
and why it occurs.
A person operating a wave generator
finds that when she sets the function
generator to 116 Hz, she sees a string
with 5 nodes.
What frequency corresponds to the 7th
harmonic?
HomeworkDue Tuesday, 6/9:
Complete the Wave Interference
Worksheet
Two Days Late:
Complete the Wave Speed Worksheet
Movement of WavesWe are going to watch two very short
clips.
I want you to compare the sound of the
train horn as it passes us by and the
sound of the racecar as it passes us by.
What do these objects have in common?
What are we hearing?
Weeee-oooooWhat we’re hearing is something known
as the Doppler Effect.
The apparent change in frequency due
to the motion of the source of the sound
is called the Doppler Effect.
If you, the receiver of the frequency, also
move – you can also experience the
Doppler Effect.
But let’s back up for a minute.
The Doppler EffectWhile this effect happens with all types of
waves, it’s easiest to talk about the
Doppler Effect when we discuss sound.
But because it’s impossible to see sound
waves, we’re going to need to create an
analogy of what’s happening.
Let’s imagine there’s a small bug
standing in the middle of a puddle, but it
is vibrating up and down, creating ripples
in the puddle.
The Doppler EffectIf the bug vibrates up and down with a
constant frequency, the waves are going
to produce concentric circles, like in this
figure:
The waves will reach points A and B at
the same time, with the same frequency.
The Doppler EffectNow imagine that the bug now travels to
point B slower than the wave travels.
The waves no longer appear as
concentric circles. The centers of the
circles now move in the direction of the
swimming bug.
The Doppler EffectAs a result, an observer at B would
encounter wave crests more often.
More waves
per second…
The observer at B encounters a higher
frequency. This again, is because the bug is
moving towards B, so B sees the waves more
frequently than if the bug were not moving.
The waves don’t travel as far.
There’s a term
for that…
The Doppler EffectAn observer at A, on the other hand,
encounters the wave at a lower
frequency.
The waves take a longer time to get to A,
as there is more of a distance the waves
need to travel to get to A.
The Doppler EffectAs a wave source moves towards an
observer, the observer encounters waves
with a higher frequency.
As the wave moves away from an
observer, the observer encounters waves
with a lower frequency.
The Doppler EffectWater waves travel across the surface of
water, but sound waves travel like a
sphere.
The Doppler effect is very noticeable
when you hear a train passing by, a car
horn, police siren, or an ambulance.
The Doppler EffectOddly enough, the Doppler effect also
occurs in light too.
When a light source approaches an
observer, there is an in the
perceived frequency.
When a light source travels away from
an observer, there is a in the
perceived frequency.
increase
decrease
The Doppler Effect
An increase in frequency is called a blue
shift, because the increase is towards
the high-frequency, or blue, end of the
spectrum.
The Doppler Effect
A decrease in frequency is called a red
shift, referring to the low-frequency, or
red, end of the spectrum.
The Doppler EffectDistant galaxies show a red shift when
they are observed.
What does that mean about the motion of
these galaxies relative to Earth?
Looking at that color, astronomers are
able to determine how quickly they’re
traveling from Earth.
The Doppler EffectRapidly spinning stars will show both a
blue shift and red shift. A blue shift will
appear on half of the planet, while the red
shift will occur on the other half.
This information tells astronomers how
fast a star is spinning.
This video explains it a bit more.
Physics Fun Fact: Radar Guns
Police officers utilize the Doppler effect in
their cars to catch speeders.
Radar guns emit microwaves towards a
moving car, which then bounce back.
The reflections are received by the gun,
and the speeder’s speed is calculated.
Doppler Effect FormulaWe have a formula that mathematically
explains what our ears and eyes
perceive.
The formula depends on your situation:
Doppler Effect FormulaIf neither your wave source or observer is
moving, will the Doppler Effect be
observed?
No.
If neither the source nor the observer are
moving, there is no change in the
apparent frequency.
Doppler Effect FormulaIf the wave source is moving towards an
observer at rest:
f ’= 𝑣
(𝑣 − 𝑣𝑠)
fWhere:
v = velocity of sound or light in medium
vs = velocity of the source
f = real frequency
f’ = apparent frequency
Doppler Effect FormulaIf the wave source is moving away from
an observer at rest:
f ’= 𝑣
(𝑣 + 𝑣𝑠)
fWhere:
v = velocity of sound or light in medium
vs = velocity of the source
f = real frequency
f’ = apparent frequency
Doppler Effect FormulaIf the observer is moving towards a
stationary wave source:
f ’= (𝑣 + 𝑣
𝑜)
𝑣f
Where:v = velocity of sound or light in medium
vo = velocity of the observer
f = real frequency
f’ = apparent frequency
Doppler Effect FormulaIf the observer is moving away from a
stationary wave source:
f ’= (𝑣 − 𝑣
𝑜)
𝑣f
Where:v = velocity of sound or light in medium
vo = velocity of the observer
f = real frequency
f’ = apparent frequency
Doppler Effect FormulaThis formula can be combined to the
following combination:
f ’= (𝑣 ± 𝑣
𝑜)
(𝑣 ∓ 𝑣𝑠)
fWhere:
v = velocity of sound or light in medium
vs = velocity of the source
vo = velocity of the observer
f = real frequency
f’ = apparent frequency
Sample ProblemsOn a 16 ⁰C day, a police car produces a
siren with a frequency of 1200 Hz while
traveling at 30 m/s towards a stationary
passerby.
What is the apparent frequency
experienced by the observer?
What frequency do they hear as the car
drives away?