unit 5: vibrations, waves & sound. simple harmonic motion position vs. time graph for an object...
TRANSCRIPT
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UNIT 5: VIBRATIONS, WAVES & SOUND
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SIMPLE HARMONIC MOTION
Position vs. time graph for an object shows how oscillations can create waves.
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PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND
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WAVES Energy transfer can occur by doing work, by heat,
or by waves! Wave: a disturbance (vibration) that travels
mechanical waves require a material medium (solid, liquid, or gas) – particles vibrate in simple harmonic motion (water, sound, earthquake waves)
electromagnetic waves travel through a material or a vacuum – vibrating electric and magnetic fields (radio, microwave, infrared, visible light, ultraviolet, x-ray, gamma rays)
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WAVES Transverse
waves: vibrations are perpendicular to wave direction
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WAVES Longitudinal
waves: vibrations parallel to wave direction
rarefaction
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WAVES Frequency, f: number of waves each second,
unit: Hertz (Hz) 1 Hz = 1 wave/sec Period, T: time between identical points on
two waves, unit: s f=1/T Wavelength, : distance between identical
points on two waves, unit: m
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WAVES Amplitude, A: maximum displacement
from equilibrium, unit: m
Wave speed, v: speed of the wave, not the particles, unit: m/s v=f use difference in wave speeds to find distance
ex: lightning & thunder
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WAVES What could affect wave speed of a
string being held tight between two points?
Wave speed is also proportional to tension and inversely proportional to μ (mass per unit length m/L)
T
v
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PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND
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WAVE INTERACTIONS Each point
on a wave travels in straight lines perpendicular to the wave front
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WAVE INTERACTIONS Reflectio
n: waves "bounce back" at boundary
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WAVE INTERACTIONS Law of Reflection: i = r i: incidence, r:
reflection
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WAVE INTERACTIONS Reflectio
n: with an open boundary
reflection is right-side-up
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WAVE INTERACTIONS Reflection
with a confined boundary
reflection is upside-down.
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WAVE INTERACTIONS Absorption:
wave energy becomes heat
Transmission: wave enters new medium, speed & change
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WAVE INTERACTIONS Interference:
waves pass through each other without changing each other, but their displacements add together
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WAVE INTERACTIONS constructive interference: combined
wave displacement is greater than individual waves
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WAVE INTERACTIONS destructive interference: combined
wave displacement is less than individual waves
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Interference Condition for constructive interference:D1 – D2 = n where n = 1, 2, 3…
Condition for destructive interference:D1 – D2 = (n+1/2) where n = 0,1, 2,
3…
D1 is distance from first source to point
D2 is distance from second source to point
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WAVE INTERACTIONS Refraction: wave path bends as wave
crosses boundary. Note that speed & wavelength change as wave moves into new
medium, but frequency remains constant.
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WAVE INTERACTIONS Refractio
n: wave bends toward the normal when it slows down
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WAVE INTERACTIONS Refractio
n: wave bends away from the normal when it speeds up
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WAVE INTERACTIONS Diffractio
n wave spreads out or “bends” beyond edge of barrier
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WAVE INTERACTIONS Diffraction
greatest when is greater than or equal to the size of opening or object
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WAVE INTERACTIONS Standing
Waves: interference of two identical waves goingopposite directions makes waves appear to vibrate in place
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WAVE INTERACTIONS Standing
Waves: nodes: no
displacement loops or
antinodes: maximum displacement
node distance = /2
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SOUND WAVES Source
: a vibrating object (vocal cord, string, reed, etc.)
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SOUND WAVES Wave type:
mechanical longitudinal graph as
transverse
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SOUND WAVES Pitch: musical tone or note – frequency of a
wave sonic spectrum:
C major scale C D E F G A B C
frequency (Hz)
264
297
330
352
396
440
495
528
musical scale: specific proportional frequencies
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MUSICAL INSTRUMENTS Stringed Instruments
string pitch = resonant vibrating frequency of string
fundamental (lowest f): string is a single loop standing wave
harmonic: integer multiple of fundamental
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MUSICAL INSTRUMENTS =2L/n
L: length of string, and n is 1,2,3…
f=v/v: wave speed in string
v=√TL/mT: tension, m: mass of string
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MUSICAL INSTRUMENTS Stringed Instruments
quality: mixture of fundamental and harmonics (makes different instruments sound different)
sound boards & boxes: more air surface contact - amplifiers
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MUSICAL INSTRUMENTS
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MUSICAL INSTRUMENTS Wind Instruments
pitch = frequency of vibration of column of air
f = v/v: sound speed in air : wavelength, depends on length of air column
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MUSICAL INSTRUMENTS open-end tube: each end of tube is
antinode = 2L/n L: length of tube and n is
1,2,3… Examples: flutes, saxophones, some
organ pipes
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MUSICAL INSTRUMENTS closed-end tube: closed end of
tube is node =4L/n L: length of tube and n is
1,3,5 Examples: clarinets, some pipe
organs
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PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND
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SOUND INTERACTIONS Echo: sound wave reflection;
maximum from rigid, smooth surfaces sonar: distance by timing pulse echoes,
x = vsoundt(repeated echoes give a "picture" of surface)
ultrasound: sonar using 1-10 MHz waves (detects smaller objects, inaudible); body vsound = 1540 m/s
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SOUND INTERACTIONS Resonance (sympathetic vibration)
objects have natural vibrating frequency
sending waves to an object at at its natural frequency will make it vibrate
pushing a child on a swing using microwaves to heat up water
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SOUND INTERACTIONS
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SOUND INTERACTIONS The
Doppler Effect: apparent change in frequency due to motion of source or listener
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SOUND INTERACTIONS The Doppler
Effect Source is moving
toward observer
C
Vf
fs
so
1
Vs = speed of sourcefo = observed frequencyfs = frequency of sourceV0 = speed of observerC = wave speed
Observer is moving toward the source
C
Vff oso 1
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SOUND INTERACTIONS The Doppler Effect
Source is moving away
Vs = speed of source fo = observed frequency fs = frequency of source V0 = speed of observer C = wave speed
CVf
fs
so
1
C
Vff oso 1
Observer moving away from the source
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Doppler Effect
Vs = speed of source fo = observed
frequency fs = frequency of source V0 = speed of observer C = wave speed
If observer and source are moving toward each other then (+/-)
If observer and source are moving away from each other then (-/+)
s
oso VC
VCff
What if both source and observer are moving?
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SOUND INTERACTIONS Radar: uses Doppler Effect in radio
waves reflected off an object to determine its speed
Red shift and Blue shift of light tells astronomers whether a star is moving toward or away from Earth.
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SOUND INTERACTIONS
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SOUND INTERACTIONS The Doppler Effect
sound barrier: “pile-up” of sound waves (pressure) in front of object traveling Mach 1
sonic boom: cone-shaped pressure pulse following an object traveling at supersonic speeds (water wake following a speedboat)
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SOUND INTERACTIONS
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PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND
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QUIZ 5.4 The speed of sound in earth is 3500 m/s. An
earthquake wave, frequency 5 Hz, travels from its source to a distant mountain range and returns in 3.4 minutes.
(a) How far away is the mountain range? (b) What is the wavelength of the earthquake
wave? (c) If the mountain range was moving away
at 0.50 m/s. what would be the frequency of the reflected wave?
357,000 m
700 m
5.00 Hz
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UNIT 5 REVIEW
f = 1/T v = f i = r
visinr =
vrsini
node dist = /2
loop height = 4A
v = 331 + 0.6T
I = P/4r2
= 10log(I/
I0)
I0 = 1×
10-12 W/m2
open pipe = 2L
closed pipe = 4L
x = vt
km
2Ts gL
2Tp
B
v
E
vmTL
v
S
Lsh vv
vvff
S
Lsh vv
vvff