physics vibrations and waves general definitions of vibrations and waves vibration: in a general...

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