Ch
14&15 Waves & Sound
Updated 5/26/03
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Vibrations:
Forced
Oscillations
Transverse Waves: http://surendranath.tripod.com/Twave/Twave01A.html
Transverse
Wave-1
Doppler Effect: http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm
Doppler
effect
Shock Waves http://www.applewoodheights.ca/Bilic/assign/SPH4A0/doppler/sonic.html
Shock Waves: Bullets http://www.aerospaceweb.org/question/aerodynamics/q0074.shtml
Oscillations
& Waves Physics
http://surendranath.tripod.com/
1
TWO METHODS OF TRANSFERRING ENERGY ARE WAVES & COLLISIONS
2
A DISTURBANCE MOVING THROUGH SPACE OR MATTER IS A WAVE.
3
a] WAVES ARE CREATED BY OBJECTS THAT VIBRATE.
b] VIBRATIONS CAN BE DESCRIBED BY THEIR FREQUENCY, PERIOD, & AMPLITUDE
c] A VIBRATION CYCLE IS ONE COMPLETE BACK & FORTH MOTION.
d] AMPLITUDE IS THE MAXIMUM DISPLACEMENT FROM REST.
e] DRAW A PENDULUM & LABEL THE VIBRATION AND AMPLITUDE.(pg 309)
/////|\\\\\
/|\
/
| \
/
| \
/
| \
/
| \
/
| \
/
| Amp \
0
|<----->0
---------------->
Vibration
<----------------
Rest Position 0
f] DRAW A VIBRATING WEIGHT & SPRING AND & LABEL THE AMPLITUDE (pg 310)
4
a] FREQUENCY (f) = # EVENTS/UNIT TIME
10.2
b] HERTZ (Hz) = 1 EVENT/SECOND
c] PERIOD (T) = THE TIME/EVENT.
d] THE MATH RELATIONSHIP BETWEEN FREQUENCY & PERIOD: T = 1/f
5*
a] A child on a swing swing completes 20 cycles in 25 s.
Find the frequency & period.
(See pg 309)
b] A stroboscope is flashing so that the time interval between flashes is
1/80
s. Find the strobe's frequency.
c] Calculate the frequency and period of a tuning fork that vibratges
24,000
times in 1.00 min.
6
a] TWO PENDULUMS ARE IN PHASE IF AT ANY GIVEN MOMENT THEY HAVE THE
SAME
displacement from rest and are
moving in the same direction.
b] DIAGRAM & LABEL 1 PAIR OF PENDULUMS IN PHASE. (Fan Demo).
/////|\\\\\ /////|\\\\\
/
/
/ |
/ |
/ /
/ Same Direction / |
/ Same Displacement /
/ |
/ |
V / d V
/ d
<---- 0<------| <----
0<------|
c] DIAGRAM & LABEL 3 PAIRS OF PENDULUMS SHOWING 3 OUT OF PHASE.
/////|\\\\\ /////|\\\\\
/
\
/ |
| \
/ Same Direction
\
/ | Different Displacement \
/
\
/ |
| \
V / d
d \ V
<---- 0<------|
|------>0<----
/////|\\\\\
/////|\\\\\
/
/
/ |
/ |
/ Different Direction /
/ Same Displacement / |
/ /
/ |
/ |
V / d
V / d
<---- 0<------|
---->0<------| &nnbsp;
/////|\\\\\ /////|\\\\\
/
\
/ |
| \
/ Different Direction \
/ | Different Displacement \
/
\
/ |
| \
V / d
d
\ V
<---- 0<------|
|------>0 ---->
7
DRAW A DIAGRAM SHOWING TRANSVERSE WAVE VECTORS THAT ARE:
a] IN PHASE; [b] 180o OUT OF PHASE;
[c] 90o OUT OF PHASE
8 DISTANCE BETWEEN CORRESPONDING POINTS ON CONSECUTIVE WAVES IS WAVELENGTH.
9
a] IN A TRANSVERSE WAVE THE DISTURBANCE (Vibration) IS PERPENDICULAR
TO
WAVE TRAVEL.
b] DRAW & LABEL DIAGRAM [13 lables, p 312].
c] TWO EXAMPLES: Light and
string waves.
Note: Strings are found
on pianos, guitars, violins, etc.
10
a] IN A LONGITUDINAL WAVE THE DISTURBANCE (Vibration) IS PARALLEL TO
WAVE
TRAVEL.
b] DRAW & LABEL DIAGRAM [5 labels, p 314].
c] STATE AN EXAMPLE: Sound Waves
Note: Water waves and
earthquakes are combinations of Transverse &
Longitudinal waves calles Surface Waves.
11
WAVE FORM | WAVELENGTH | BEATS | TIME |
FREQUENCY | LAMBDA x f
|<---------3m--------->| lambda
| |
| beats/time|
----------------------------------------------------------------------------
b] Two forms of the wave equation are: Speed = Wavelength x Frequency
Speed = Wavelength/Period
c] THE SPEED OF THE WAVE DEPENDS ON THE MEDIUM AND IS INDEPENDENT OF THE
FREQUENCY WHICH IS DETERMINED BY THE SOURCE.
12
a] Find the period for a 1.3 m string wave traveling at 2.5 m/s.
b] Sound travels at 350 m/s, find the wavelength for middle C (256 Hz)
c] A water wave needs 5.2 s to travel 19 m.
It takes 17 s for 20 waves
to pass. Find the wave's
wavelength.
d] Find the speed of the 283 m, 1060 kHz radio waves.
(see pg 316)
e] The speed of sound is 331 m/s + 0.59T. If
the temp is 25oC, what frequency does a bat need to capture a 2 mm insect?
13
IF 15 CRESTS PASS A POINT IN 4 SECONDS, FIND:
a
THE WAVELENGTH
c TIME BETWEEN WAVE CRESTS
b
THE FREQUENCY d
THE VELOCITY
|<------------------ 24 cm ----------------->|
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
a] Lambda = 24 cm/3 waves = 8 cm/wave
b] f = 15 waves/4 sec = 3.75 waves/sec
c] T = 4 sec/15 waves = 0.267 sec/wave
d] S = f x lambda = 3.75 waves/sec x 8 cm/wave = 30 cm/sec
13P
IF 21 CRESTS PASS A POINT IN 3 SECONDS.
|<---------------------- 20 m
---------------------->|
|
|
|
|
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
a] Lambda = 20 cm/3.5 waves = 5.71 cm/wave
b] f = 21 waves/3 sec = 7 waves/sec
c] T = 7 sec/21 waves = 0.333 sec/wave
d] S = f x lambda = 7 waves/sec x 5.71 cm/wave = 40 cm/sec
14
a] DRAW & LABEL THE DIAGRAM FOR THE LAW OF REFLECTION.
(pg 418)
b] LAW OF REFLECTION: Angle of Reflection = Angle of Incidence.
10.5
15
THE WAVE MUST HAVE THE SAME FREQUENCY IN THE NEW MEDIUM AS IN THE OLD.
SINCE THE SPEED CHANGES THE WAVELENGTH ADJUSTS.
[pg 317]
16
DRAW THE WAVES PULSES HITTING MORE & LESS DENSE MEDIUMS.
ARE THEY
a] FAST OR SLOW
d] ERECT OR INVERTED
b] FREQUENCY & WAVELENGTH EQUATIONS
e] SAME OR REDUCED AMPLITUDE
c] REFLECTED OR TRANSMITTED
f] SHORTER OR LONGER LAMBDA
17
DRAW A WAVEFRONT DIAGRAM AND THE CORRESPONDING WAVE RAY FOR:
a] A SERIES OF STRAIGHT WAVES. [b]
A SERIES OF CIRCULAR WAVES.
c] A STRAIGHT WAVE REFLECTED FROM A FLAT SURFACE. (pg 319)
18
DRAW A DIAGRAM FOR RAYS REFLECTED BETWEEN A PARABOLIC TRANSMITTER & A
PARABOLIC RECEIVER.
19
Interference occurs when two or more waves act simultaneously on the same
particle.
The Principle of Superposition: the
result displacement is the algebraic
sum of the individual displacements.
20
DRAW BEFORE, DURING, & AFTER DIAGRAMS SHOWING
a] CONSTRUCTIVE INTERFERENCE OF 2 UNEQUAL PULSES.
b] DESTRUCTIVE INTERFERENCE OF 2 UNEQUAL PULSES.
c] DESTRUCTIVE INTERFERENCE OF 2 EQUAL PULSES.
21
a] AFTER 2 PULSES PASS THROUGH ONE ANOTHER, THEY RESUME THEIR ORIGINAL
SHAPE.
b] THE MEDIUM IS UNDISTURBED DURING THE MEETING OF TWO EQUAL AND OPPOSITE
PULSES.
22
a] DRAW FOUR 5 m STANDING WAVE FORMS AND FIND THEIR WAVELENGTHS.
b] Find the speed for a 12 Hz standing wave.
|<---------6m--------->|
3/2 Lambda = 6 m
|
|
Multiply both sides by 2/3
|
| Lambda =
2/3 x 6 m = 4 m
------------------------
S = Lambda x f =
= 4 m/wave x 12 waves/sec
= 48 m/s
23
DIFFRACTION: The bending of a wave around a barrier.
DIAGRAM Labels: fronts, Lambda,
Barrier, D, D approximates Lambda.
24
a] DOUBLE SLIT DIFFRACTION: the
bending of a wave around a barrier.
If the distance between slits & the slit size is approximately
equal to the wavelength then each slit acts as if it was a point
source and circular wave come from it.
b] FOUR USES:
i]
Diffraction proves that light and X-rays are waves.
ii] X-Ray
diffraction is used to find the structure of proteins.
iii] Diffraction is
used to determine the elements in compounds
iv] Diffraction
limits the ability of microscopes and telescopes
to distinguish between two close objects.
Resolving power.
Ex #1: as you enlarge (magnify) a picture it gets grainer
(looses resolution)
Ex #2: the resolution on small TV's & telescopes is better
than large TV's, i.e., you get a sharper picture.
c] Draw a diagram of the interference pattern between two point sources
in
phase. See lab.
Labels: [1] fronts, [2] Lambda, [3]
Barrier, [4] D,
[5] D approximates Lambda, [6 & 7] Constructive interference lines,
[8] Central bright, [9 & 10] Primary brights, [11] X, [12] L
d] Constructive and destructive interference causes this pattern.
25
a] DOPPLER EFFECT: The apparent change in frequency due to the motion of the
source or the observer. f2 = f1 V/(V+Vs),
V = cΔf/f (pg 396)
b] DIAGRAM Labels: [1] V = 0, [2] c
> V > 0, [3] c = wave speed
[4 & 5] Lambda Long & f Low, [6 & 7] Lambda short & f high.
c] Traffic control, find the speed of galaxies (red shift).
d] V = cΔf/f = 3.0 x 108 m/s x 2000 Hz/9.375 x 109 Hz
= 6,000 m/s /9.375 x 101
= 64 m/s x 1 mi/h/0.447 m/s = 143 mi/h
26
What happens to the apparent frequency for the following situations:
a] The listener is stationary & the source is approaching. f increases
b] The listener is stationary & the source is receding.
f decreases
c] The source is stationary & the listener is approaching. f increases
d] The source is stationary & the listener is receding.
f decreases
27
a] Resonance occurs between two objects when a vibration of one object at
the correct frequency induces a large vibration of the other.
b] Objects resonating with each other.
1] A child's body with a
spring.
2] Atoms in a molecule with
infrared light.
3] A radio's circuit with
the signal
Doppler
Effect &
SHOCK WAVES
Updated 5/26/03, See Handout
Top
Vo = Observer Velocity
Vs = Source Velocity
c = Wave Velocity
Vs
= 0
*
DOPPLER EFFECT
c > Vs > 0
c
+ Vo
fo
= ------ x fs
Vo
l Vs
c
+ Vs
*----> |<---->| *
* * *->-----
|
| |
c/\f
|
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Vs = ---
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f
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|<-----cT------>|<--Vt-->|
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*
* *
* |
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Vs
= c
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SHOCK WAVE |
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(Mach Cone)
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|<-----cT------>|<-----Vt------>|| |
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SHOCK WAVE |
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(Mach Cone)
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|<-----cT------>|<-----Vt------>|
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