wave motion - central bucks school district€¦ · factor affecting wave speed remember… the...
TRANSCRIPT
WHAT IS A WAVE?
A disturbance that transfers energy, not matter,
through space.
Pulse – a single disturbance moving through a
medium (a substance or material which carries a wave).
Wave – a repeating disturbance moving
through a medium.
THE ANATOMY OF A WAVE
Dashed line – the rest position, no disturbances
Crest – maximum upward displacement.
Trough – maximum downward displacement.
Amplitude – maximum displacement (height of wave); amount of energy a wave carries.
Wavelength – The distance between 2 successive points in phase.
A transverse wave
FREQUENCY & PERIOD
Frequency (symbol = f)
The number of complete vibrational cycles of a medium per a given amount of time.
i.e. cycles/second, waves/second, vibrations/second,
Units: Hertz (Hz)- cycles per second
Period (symbol = T)\
The time for a particle on a medium to make one complete vibrational cycle. Units: Second
T = 1 f = 1f T
PRACTICE
Ocean waves are timed to have traveled one
wave length in 3.44 s. What is the frequency of
the waves?
A car tire revolves with a frequency of 10 Hz.
How long does one revolution take?
TYPES OF WAVES
Transverse Waves
A wave that occurs when the medium (spring,
water, rope, etc.) moves or vibrates perpendicular
(90) to the direction of the wave motion.
TYPES OF WAVES
Longitudinal Waves
A wave in which particles of the medium move in a
direction parallel to the direction which the wave
moves.
TYPES OF WAVES
Surface Waves
A wave in which particles of the medium undergo
a circular motion. These waves are neither
longitudinal nor transverse.
TYPES OF LABS
3 types
Find a mathematical relationship
Determine a value
Test an already understood statement/law
For mathematical relationship labs, the objective
is always stated as:
Find the mathematical relationship between
_dependent_and _independent_ variables of the
object.
STEPS/REQUIREMENTS FOR M.R. LABS:
State your objective
First variable in statement is always the dependent (y-axis) variable
You will most likely measure this value, it is what you are testing
Second variable in statement is always the independent (x-axis) variable
You determine and control this variable
Collect your data in a chart
Graph your data, find the Line of Best Fit (LBF)
Use the LBF to determine the TE and MRS
TE –Translated Equation
MRS – Mathematical Relationship Statement
Translated Equation: stating the relationship of
the two variables in an equation for future
calculations and relating
Use the general form from your WS to help you
Mathematical Relationship Statement: a
written sentence that states how the variables
relate
Used to help describe with words
DETERMINING THE M.R. BETWEEN THE
WAVELENGTH AND FREQUENCY OF A WAVE
Objective:
Determine the mathematical relationship between
the wavelength of a wave and the frequency of that
wave.
WHAT IS THE MATHEMATICAL RELATIONSHIP
BETWEEN WAVELENGTH AND FREQUENCY?
Wavelength is inversely proportional to
frequency
Translated equation:𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ =(𝑛𝑢𝑚𝑏𝑒𝑟)
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
What are the units for the constant in your TE?
m/s: This is speed!!!!!!
THE WAVE SPEED EQUATION
Speed = wavelength frequency
v = f(m/s) (m) (Hz = 1/s)
A sound wave has a frequency of 262 Hz and a wavelength measured at 1.29 m.
a) What is the speed of the wave?
b) How long will it take to travel the length of a 91.4-m football field.
c) What is the period of the wave?
FACTORS AFFECTING WAVE SPEED
Remember…. Speed = distance/time
Speed of a Wave
TrialTension
(N)
Frequency
(Hz)
Wavelength
(m)
Speed
(m/s)
1 2.0 4.05 4.00 16.2
2 2.0 8.03 2.00 16.1
3 2.0 12.30 1.33 16.4
4 2.0 16.2 1.00 16.2
5 2.0 20.2 0.800 16.2
6 5.0 12.8 2.00 25.6
7 5.0 19.3 1.33 25.7
8 5.0 25.5 1.00 25.5
FACTORS AFFECTING WAVE SPEED
The speed of a wave does not depend on the
amplitude (height/energy) of the wave.
The speed of a wave does depend on the
medium through which the wave is moving.
BEHAVIOR OF WAVES
Wave Interference
The phenomenon which occurs when 2 waves meet while traveling along the same medium.
Principle of superposition
When 2 waves interfere, they combine to form a new wave, which is the algebraic sum of the displacements of the individual waves at the same location. The waves continue to pass through one another after the interference.
BEHAVIOR OF WAVES, CONTINUED…
Constructive Interference
Occurs when interfering waves have displacements in the same direction. crest – crest trough – trough
Amplitudes add
BEHAVIOR OF WAVES, CONTINUED…
Destructive Interference
Occurs when interfering waves have
displacements in the opposite direction.
crest – trough
Amplitudes subtract
BEHAVIOR OF WAVES, CONTINUED…
Two Source Interference Twin water bugs Jimminy and Johnny are both creating a series of circular waves by jiggling their legs in the water. The waves undergo interference and create the pattern represented in the diagram at the left. The thick lines in the diagram represent wave crests and the thin lines represent wave troughs. Several of positions in the water are labeled with a letter. Categorize each labeled position as being a position where either constructive or destructive interference occurs.
A crest of amplitude 6 cm meets an opposing
crest of amplitude 4 cm. What is the amplitude
when the two waves interfere? Draw the resulting
wave diagram.
BEHAVIOR OF WAVES, CONTINUED…
A crest of amplitude 11 cm meets an opposing
trough of amplitude 8 cm. What is the amplitude
when the two waves interfere? Draw the resulting
wave diagram.
BEHAVIOR OF WAVES, CONTINUED…
BEHAVIOR OF WAVES, CONTINUED…
Reflection
When waves reach a
barrier they bounce
off and head in a
different direction.
The angle at which the
waves approach the
barrier will always
equal the angle at
which they reflect off
the barrier.
BEHAVIOR OF WAVES, CONTINUED…
Refraction
Involves a change in
direction of the
waves as they pass
from one medium to
another.
As the wave bends,
a change in speed
and wavelength also
occurs.
BEHAVIOR OF WAVES, CONTINUED…
Diffraction
Involves a change in
direction of waves as
they pass through an
opening or around a
barrier in their path.
i.e., waves in a harbor
bend around boats or
hearing someone
speaking from an
adjacent room.
THE NATURE OF A SOUND WAVE
Sound is a wave that is created by a vibrating
source that creates disturbances in surrounding
air molecules.
Sound needs a medium to travel from one location
to another, thus it is a mechanical wave.
For sound traveling through air, the vibrations of
the particles are best described as longitudinal.
THE NATURE OF A SOUND WAVE, CONTINUED…
Because of the
longitudinal motion of
the air particles, there
are regions in the air
where air particles are
compressed together
(compressions) and
other regions where the
air particles are spread
apart (rarefactions).
BEHAVIOR OF SOUND WAVES
Constructive interference occurs when either 2
compressions or 2 rarefactions meet. If there is
continuous reinforcement a very loud sound is
produced (antinodes).
Destructive interference occurs when
compressions meet rarefactions. If there is
continuous canceling, no sound will be heard
(nodes).
BEHAVIOR OF SOUND WAVES, CONTINUED
Two Source Sound
InterferenceThick lines = compressions
Thin line = rarefactions
SOUND PROPERTIES
As sound moves through a medium, each particle of the medium vibrates at the same frequency.
Pitch – the sensation of frequencies high pitch = high frequency low pitch = low frequency
Intensity – the amount of energy transported large amplitude = high intensity (louder*) small amplitude = low intensity (softer*)
* The loudness of a sound is subjective. The same sound will not be perceived to have the same loudness to all individuals.
VOLUME
Intensity is the amount of energy transported past a given area of medium per unit of time
Intensity = Energy /(time * area) or (since Power=Energy/time)…
Intensity = Power/ Area
Volume is based on a logarithmic scale of base 10 in intesity
Volume is measured in Decibels
0 Decibels (dB) is considered the “Threshold of Hearing”
VOLUME EXAMPLESSource Intensity IntensityLevel # of TimesGreater Than TOH
Threshold of Hearing (TOH) 1*10-12 W/m2 0 dB 100
Rustling Leaves 1*10-11 W/m2 10 dB 101
Whisper 1*10-10 W/m2 20 dB 102
Normal Conversation 1*10-6 W/m2 60 dB 106
Busy Street Traffic 1*10-5 W/m2 70 dB 107
Vacuum Cleaner 1*10-4 W/m2 80 dB 108
Large Orchestra 6.3*10-3 W/m2 98 dB 109.8
Walkman at Maximum Level 1*10-2 W/m2 100 dB 1010
Front Rows of Rock Concert 1*10-1 W/m2 110 dB 1011
Threshold of Pain 1*101 W/m2 130 dB 1013
Military Jet Takeoff 1*102 W/m2 140 dB 1014
Instant Perforation of
Eardrum1*104 W/m2 160 dB 1016
THE SPEED OF SOUND
Speed = distance/time
v = x / t
A tuning fork produces a sound wave in air with
a frequency of 261.6 Hz. At room temperature
the speed of sound is 343 m/s. What is the
wavelength?
FACTOR AFFECTING WAVE SPEED
Remember… the speed of any wave depends upon
the properties of the medium through which the
wave is traveling.
Looking at the elastic properties (maintaining
shape) and the inertial properties the following
pattern can be observed:
vsolids > vliquids > vgases
Sound travels slower in cool air than in warm air.
BEHAVIOR OF SOUND WAVES
Resonance
Occurs when one object vibrating at the same natural frequency of a second object forces the second object into vibrational motion.
The result of resonance is always a big vibration –a loud sound!
Resonance is the cause of sound production in musical instruments.
DOPPLER EFFECT
Occurs whenever the source of waves is moving with respect to an observer.
There is an apparent upward shift (higher frequency = higher pitch) for observers whom the source is approaching.
There is an apparent downward shift (lower frequency = lower pitch) for observers whom the source is receding.
STANDING WAVES
A pattern that results when a wave is confined to a given space in a medium.
The wave pattern is only produced when one end of the rope is vibrated at just the right frequency.
Nodes – areas of no displacement
(destructive interference)
Antinodes – areas of maximum displacement
(constructive interference)