AP Physics B Ch 11 and 12
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Transcript of AP Physics B Ch 11 and 12
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Waves transfer energy NOT matter
Two categories of waves
Mechanical Waves
± require a medium (matter) to transfer wave energy
Electromagnetic waves
± no medium required to transfer wave energy
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Mechanical Waves Two types based on vibration direction
± transverse
± longitudinal
Transverse ± vibrating Perpendicular to velocity direction
Longitudinal ± vibrating Parallel to velocity direction
transverse
longitudinal
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5 Wave Properties Velocity (v) meters/second
Wavelength (P lambda) meters ± straight line peak to peak distance for one full wave cycle
Frequency (f) Hertz
± # of wave cycles passing a fixed point per second
Period (T) seconds
± # of seconds for one full wave cycle to pass a fixed point Amplitude (A) in units of wave displacement
± measure of the energy transferred by the wave
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Wave Equation
v = f P ± velocity = frequency x wavelength
What does wave speed depend on?
Wave velocity DOES NOT depend on
frequency or wavelengthMedium type and its properties determine
wave speed
#
sec sec
meters of waves meters x
ond ond wave!
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Wave Source Controls Frequency
hand motion sets wave frequency of rope waves
speaker controls frequency of sound waves
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Frequency ± Wavelength Relationship
frequency is NOT speed
equations for calculations
#
sec
wave cycles frequency
ond
!# wave travels
sec
of meters speed
ond !
d
v t ! v T
P
!1
f T !v f P!
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Frequency ± Wavelength Relationship
Inverse relationship between frequency
and wavelength
v f P!
constant for fixed
medium properties when frequencyincreases
length of each wave
decreases
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Change frequency at the source
Change velocity by changing medium
Two ways to change wavelength
v f
P !
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11-11 Reflection and Transmission of Waves
A wave reaching the endof its medium, but where
the medium is still free
to move, will be reflected
(b), and its reflection will
be upright.
A wave hitting an obstacle will be
reflected (a), and its reflection will be
inverted.
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11
Law of Reflection angle of incidence U
i= angle of reflection Ur
angles measured from the rays to the normal
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Wave Interference
Wave pulses are energy not matter When pulses ³collide´ they overlap briefly
Superposition principle
± wave pulses can co-exist at the same pointin a medium at the same time
± they pass through without affecting each
other
± overlapping pulses: the resultantdisplacement of the medium is the algebraic
(+/) sum of the pulse amplitudes
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Constructive Interference
Two + amplitude pulses
(upright) approaching
Total displacement is sum of
individual pulses
After interference each pulse isunchanged
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Destructive Interference
+ amplitude, amplitude
pulses approach
complete destructive
interference
pulses unchanged after
interference
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Resonance A condition resulting in large amplitude oscillation
(vibration) from a small amplitude input vibration or force
Occurs only at specific ³natural frequencies´
Natural frequency determined by characteristics of the
oscillating medium
± Length and medium properties
± series of natural frequencies exist for that medium
Examples
± child on a swing
± wave apparatus
± pendulum
± tuning forks
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11-13 Standing Waves; Resonance
Standing waves occur when both ends of a
string are fixed. In that
case, only waves which
are motionless at theends of the string can
persist. There are nodes,
where the amplitude is
always zero, andantinodes, where the
amplitude varies from
zero to the maximum
value.
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Standing Wave Formation
Constructive Interferencecreates antinodes Destructive interferencecreates nodes
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11-13 Standing Waves; Resonance
The frequencies of the
standing waves on a
particular string are calledresonant frequencies.
They are also referred to as
the fundamental and
harmonics.
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11-13 Standing Waves; Resonance
The wavelengths and frequencies of standingwaves are:
(11-19a)
(11-19b)
fundamental is lowest resonant frequency n = 1
higher harmonics are integer multiples of fundamental
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Sound Waves
Mechanical ± requires a medium Longitudinal oscillations in air pressure
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Resonance in columns of air
Open-pipe resonator
Resonant frequency
formula is the same aswith a rope
f 1 = fundamental
higher harmonics are
integer multiples of f 1
n = 1, 2, 3, 4«
2n
nv f
L!
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Not all harmonics form
due to reflection fromclosed end
f 1 = fundamental
higher harmonics are
integer multiples of f 1
n = 1, 3, 5
4n
nv f
L!
Closed pipe resonator
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12-6 Interference of Sound Waves; Beats
Sound waves interfere in the sameway that other waves do in space.
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12-6 Interference of Sound Waves; Beats
Waves can also interfere in time, causing a
phenomenon called beats. Beats are the slow³envelope´ around two waves that are relatively
close in frequency.
Beat frequency = difference in frequencies
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Doppler Effect
Change in frequency (pitch) that isperceived by an observer because of relative motion between sound source andobserver
³eee-yow´ You MUST distinguish between cause and
effect
± Cause: compression or expansion of wavelength due to relative motion
± Effect: Ear hears higher or lower pitch
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Doppler Effect ± Stationary Observer
Source approaching observer: shorter wavelength results in pitch
heard by observer being higher than actual
Source moving away from observer: longer wavelength results in
pitch heard by observer being lower than actual
(343 )'
(343 )
obs source
source
v f f
v
« »s! v¬ ¼s- ½