PHYSICS PHYSICS Vibrations and Waves
Jan 21, 2016
PHYSICSPHYSICS
Vibrations and Waves
General definitions of vibrations General definitions of vibrations and wavesand waves
VibrationVibration: in a general sense, anything that switches : in a general sense, anything that switches back and forth, to and fro, side to side, in and out, off back and forth, to and fro, side to side, in and out, off and on, loud and soft, or up and down is and on, loud and soft, or up and down is vibratingvibrating. A . A vibration is a wiggle in vibration is a wiggle in timetime..
WaveWave: a wiggle in both : a wiggle in both spacespace and and timetime is a wave. A is a wave. A wave extends from one place to another.wave extends from one place to another.
Vibrations and waves: the source of all waves is Vibrations and waves: the source of all waves is something that is vibrating. Waves are propagations of something that is vibrating. Waves are propagations of vibrations throughout space. vibrations throughout space.
1.1. VIBRATION OF A PENDULUMVIBRATION OF A PENDULUM
T l g2
What does the period (T) depend upon? Length of the pendulum (l). Acceleration due to gravity
(g). Period does not depend
upon the bob mass or the amplitude of the swing.
Vibration of a pendulum. The to-and-fro vibratory motion is also called oscillatory motion (or oscillation).
When oscillations are small, the motion
is called simple harmonic motion (shm)
and can be described by a simple sine
curve.
Wave PropertiesWave PropertiesWavelengthWavelength
Wavelength,Wavelength,, is the distance between , is the distance between two two consecutive peaks.consecutive peaks.
Wave PropertiesWave PropertiesAmplitudeAmplitude
Amplitude is the height of the wave above Amplitude is the height of the wave above or or below the equilibrium point.below the equilibrium point.
Wave PropertiesWave PropertiesPeriodPeriod
The wave period, P, this the time it take one wave to pass The wave period, P, this the time it take one wave to pass the observer.the observer.
Wave PropertiesWave PropertiesFrequencyFrequency
Frequency, f, is the number of waves passing Frequency, f, is the number of waves passing a particular point in one second.a particular point in one second.
Examples of FrequencyExamples of Frequency
What is the frequency of the second hand What is the frequency of the second hand of a clock?of a clock?
Frequency = 1cycle/60 secFrequency = 1cycle/60 sec Period = 60 secPeriod = 60 sec
What is the frequency of US Presidential What is the frequency of US Presidential elections?elections?
Frequency = 1 election/4 yrsFrequency = 1 election/4 yrs Period = 4 yrsPeriod = 4 yrs
T 1T
f
T
f
T
fT
f Tf fTf
In symbolic formIn symbolic form
oror
f
Wave Motion, Speed, Type Wave Motion, Speed, Type Waves to transfer energy, not matter, from one place to Waves to transfer energy, not matter, from one place to
anotheranotherA Vibrating source transfers a disturbanceA Vibrating source transfers a disturbanceSpeed depends on type of vibrating source and medium Speed depends on type of vibrating source and medium
through which it travelsthrough which it travelsWave speed = Wave speed = ff x x The same type of wave moves at the same speed The same type of wave moves at the same speed
regardless of regardless of ff or or For any wave, For any wave, ff is inversely proportional is inversely proportional to to
Wave TypeWave Type
Transverse waves vibrate across from Transverse waves vibrate across from direction of traveldirection of travel
Longitudinal waves vibrate along the Longitudinal waves vibrate along the direction of travel (as in a spring)direction of travel (as in a spring)
Sound WavesSound Waves
Molecules in the air vibrate about some average position creating the compressions and rarefactions. We call the frequency of sound the pitch.
Wave InterferenceWave Interference
When two wave pass each other their When two wave pass each other their superpositionsuperposition
causes reinforcement or cancellation.causes reinforcement or cancellation.
Constructive interferenceConstructive interferenceReinforcement when the crest of one Reinforcement when the crest of one
wave overlaps the crest of another wave overlaps the crest of another Their individual effects adds together, Their individual effects adds together,
resulting in a wave increased in resulting in a wave increased in amplitudeamplitude
Destructive InterferenceDestructive InterferenceCancellation when crest of one wave overlaps trough Cancellation when crest of one wave overlaps trough
of another reducing their individual effectsof another reducing their individual effectsWater waves show these bestWater waves show these best
Out of phase- the crest of one wave arrives at a Out of phase- the crest of one wave arrives at a point at the same time as a trough of the second point at the same time as a trough of the second wave arrives, effects cancel each other wave arrives, effects cancel each other In phase- two waves crests and troughs arrive at a In phase- two waves crests and troughs arrive at a place at the same time, effects reinforce each otherplace at the same time, effects reinforce each other
Sound Wave InterferenceSound Wave Interference
•Interference occurs when two sounds of difference frequency are heard superposed. •Constructive interference causes louder sound and destructive inference cause fainter sound.•This alternating pattern produces a beat. A piano tuners listens for beats to disappear.
Water Wave InterferenceWater Wave Interference
Left side is theoretical drawing of an Left side is theoretical drawing of an interference pattern.interference pattern.
Right side is the actual interference pattern.Right side is the actual interference pattern.
Standing WavesStanding WavesOccurs when a wave reflects upon itself and Occurs when a wave reflects upon itself and
interference causes the patterninterference causes the patternNodes remain stationary Nodes remain stationary
Anti nodes-occur half way between nodesAnti nodes-occur half way between nodes
Standing WavesStanding WavesChange the frequency in a standing wave and more nodes/antinodes appear in the event
8.8. DOPPLER EFFECTDOPPLER EFFECT
Refers to the change in frequency when there is relative motion between an observer of waves and the source of the waves
Doppler with SoundDoppler with Sound
Doppler with Water
The Doppler effect-The Doppler effect-Change in frequency due to the source or receiver Change in frequency due to the source or receiver
greater the speed the source, greater the Doppler greater the speed the source, greater the Doppler effecteffect Stationary bug Stationary bug
Bug swimmingBug swimming
Blue Shift-increase in frequency Blue Shift-increase in frequency Red Shift- Decrease in frequencyRed Shift- Decrease in frequency
Doppler Shift Gives Radial Doppler Shift Gives Radial VelocityVelocity
Radar
True Velocity
Tangential Velocity
Radial Velocity
Compare these spectra.Compare these spectra.
Spectrum of Hydrogen in Lab
Spectrum a Star
What do these spectra tell us about the star?
Bow wavesBow waves
V-shaped pattern made by overlapping crestV-shaped pattern made by overlapping crest
Shock Waves Shock Waves Produced by supersonic Produced by supersonic
aircraft, three-dimensional aircraft, three-dimensional cone shapedcone shaped
Sonic boom – sharp crack Sonic boom – sharp crack heard when conical shell of heard when conical shell of compressed air that sweeps compressed air that sweeps behind a supersonic aircraft behind a supersonic aircraft reaches listeners on the reaches listeners on the ground below.ground below.
SupersonicSupersonic
- slower than the speed of sound
SubsonicSubsonic
Supersonic - faster than the speed of sound
Mach Number =speed of soundspeed of object
Review QuestionsReview Questions
1. Doubling the mass of a 1. Doubling the mass of a simple pendulum undergoing simple pendulum undergoing
small oscillations does what to small oscillations does what to the period of the pendulum?the period of the pendulum?
(a) cuts it in half
(b) increases it by the square of 2
(c) nothing
(d) doubles it
(c) nothing
2. What dictates the frequency 2. What dictates the frequency of a sound wave? of a sound wave?
(a) wavelength
(b) medium
(c) source of the sound
(d) speed
(e) amplitude
(c) source of the sound
3. What determines the speed 3. What determines the speed of a wave? of a wave?
(a) the frequency
(b) the wavelength
(c) the amplitude
(d) the period
(e) the medium of transmission(e) the medium of transmission
4. A skipper on a boat notices 4. A skipper on a boat notices wave crests passing his anchor wave crests passing his anchor chain every 5 seconds. If the chain every 5 seconds. If the wave crests are 15 m apart, wave crests are 15 m apart,
what is the speed of the water what is the speed of the water waves in m/s? waves in m/s?
(a) 5 (d) 10
(b) 15 (e) 3
(c) 75
(e) 3
5. For a medium transmitting a 5. For a medium transmitting a longitudinal wave, the areas of longitudinal wave, the areas of the medium where the density the medium where the density of the medium is temporarily of the medium is temporarily
increased are called...increased are called...
(a) rarefactions
(b) compressions
(c) density holes
(b) compressions
When you move away from a When you move away from a fixed source of sound, the fixed source of sound, the
frequency of the sound you frequency of the sound you hear...hear...
(a) is greater than what the source emits
(b) is less than what the source emits
(c) is the same as what the source emits
(b) is less than what the source emits
Sonic booms from a plane are Sonic booms from a plane are produced...produced...
(a) because the plane breaks through the sound
barrier.
(b) when the plane reaches the speed of sound.
(c) by the plane traveling faster than the speed of
sound.
(d) by the plane traveling slower than the speed
of sound.
(c) by the plane traveling faster than the speed of
sound