SIMPLE HARMONIC MOTION BALL IN A BOWL PENDULUM WATER WAVES SPRINGS GUITAR STRINGS SOUND LIGHT
Dec 25, 2015
SIMPLE HARMONIC MOTION
BALL IN A BOWLPENDULUM
WATER WAVESSPRINGS
GUITAR STRINGSSOUNDLIGHT
WAVES
ONE DIMENSIONAL WAVES
CAN BE: PULSECONTINUOUSSTANDING
WAVES
LONGITUDINAL WAVESSLINKYSOUND
P-SEISMIC WAVES
TRANSVERSE WAVESSTRINGWATERLIGHT
S-SEISMIC WAVESOFTEN SINUSOIDAL (SINE WAVES)
MEASURES OF WAVES
AMPLITUDE: ENERGY IN THE WAVE
PERIOD: TIME BETWEEN PEAKS
FREQUENCY: CYCLES PER SECOND
SPEED = WAVELENGTH X FREQUENCY
WAVELENGTH: DISTANCE BETWEEN PEAKS
SPEED OF SOUND
• HOW WOULD YOU DESIGN AN EXPERIMENT TO MEASURE THE SPEED OF SOUND?
• WHAT FACTORS WOULD CONTRIBUTE TO EXPERIMENTAL ERROR?
HOW CLOSE WAS THAT LIGHTNING BOLT?
SOUND TRAVELS 700 mphin air at sea level
700 mph = 0.2 mps
Or: 5 second to travel one mile
How close was the lightning strike?Start counting off seconds after the bolt
until you hear the thunder (1 mile for every 5 sec).
INTERFERENCEWAVES WILL PASS THROUGH EACH OTHER WITHOUT PERMANENT EFFECT
THE MEDIUM MUST REACT TO THE SUM OF THE TWO (OR MORE) WAVES
IF THE PEAKS CORRESPOND: AMPLIFICATIONIF PEAK AND NODE CORRESPOND: REDUCTIONIF PEAK AND ANTI-PEAK CORRESPOND: A NODE
WHAT WOULD HAPPEN IF THERE WERE WAVE-MAKERS AT OPPOSITE ENDS OF THE WAVEPOOL?
SOUND IN A STRING
SPEED OF WAVE DEPENDS ON:
DENSITY OF STRINGCROSS-SECTION OF STRINGTENSION IN STRING
STANDING WAVES
SKIPPING ROPE
GUITAR STRING
TUNING A GUITAR STRING
CAN YOU HEAR THE BEAT?
STANDING WAVES
First harmonic
Second harmonic
Third harmonic
node
loop
WIND INSTRUMENTS
L = 3 0 /4
Flute, oboe, beer-bottle, organ...
DOPPLER SHIFT
WHEN A WAVE TRAVELS THROUGH A MEDIUMITS SPEED IS AFFECTED BY THE NATURE OF THAT MEDIUM. FOR EXAMPLE SOUND TRAVELS FASTER IN WATER OR STEEL THAN IN AIR.
IF THE SOURCE OF THE SOUND VIBRATION IS ALSO TRAVELLING THIS WILL AFFECT THE PITCH, OR FREQUENCY OF THE WAVE, SINCE THE PEAKS WILL BE CLOSER OR FURTHER APART.
DOPPLER SHIFT
SOURCE
LISTENER
SOURCE APPROACHING
SOURCE RECEDING
ENERGY IN WAVES
PARTICLES IN THE MEDIUM (STRING)MOVE AS THE WAVE PASSES
PE = 1/2 k x2
x is displacement
KE = 1/2 m v2
v = velocity or frequency
POWER IN WAVE = AMPLITUDE2
POWER IN WAVE = FREQUENCY2
BREAKING THE SOUND BARRIER
AS THE PLANE APPROACHES THE SPEED OF SOUND, WHAT HAPPENS THE SOUNDENERGY EMITTED BY THE PLANE IN A FORWARD DIRECTION?
CHANGE IN AMPLITUDE?CHANGE IN FREQUENCY?INCREASED ENERGY?
HEARING DECIBELS
VOLUME OF SOUND = 10 log (I/Io)
Whisper ~50 dbconversation ~ 70 dbpain threshold ~ 120 db
Like the Richter scale for earthquakes
2 bel is 10 times one bel,3 bel is 100 times one belone decibel is one bel/10
ELECTROMAGNETIC RADIATION
WHAT IS THE MEDIUM FOR LIGHT?
THE EM SPECTRUM IS MUCH WIDER THAN THE VISIBLE SPECTRUM
...GAMMA-X-UV-VISIBLE-IR-MICROWAVE-RADIO...
violet - blue - green - yellow - orange - red
SNELL’S LAW
a
a
mirror
a
OPTICS
SNELLS LAWMIRRORSPRISMS AND LENSES
REFRACTION
REFLECTION
n=1
n=1.33
air
glass
Light always finds the “least time” path
TWO DIMENSIONAL WAVES
WAVEFRONTS
DIFFRACTION AND INTERFERENCE
TWO-SLIT EXPERIMENT
INTERFERENCE FRINGES
COLOURS IN AN OIL-SLICK
ACTS LIKE A PRISM, IN REFLECTION
WAVES CONSTRUCTIVELY OR DESTRUCTIVELYINTERFERE WITH EACH OTHER
INTERFERENCE
DIFFRACTION GRATINGS
CAN ALSO GET INTERFERENCE FROM A REGULAR SPACED ARRAY OF LINES
OR AN ARRAY OF ATOMS IN A CRYSTAL
ONE-SLIT????
N+1-wavelengthsreinforcing
cancelling
N wavelengths reinforcing
cancelling
N+1/2 wavelengths
TWO-SLIT EXPERIMENT
CURVED MIRRORS
F
LENSES
LENSES (2)
INTERNAL REFLECTION
A
A’
C’
B’
B
C
Brewster’s angle
FIBRE OPTICS
CORE
CLADDING
n
n’ > n