What is a wave?A wave is the motion of a disturbance.

What is a wave?The medium is the physical

environment through which a disturbance can travel.

A mechanical wave is a wave that requires a medium.

Some waves do not require a medium; electromagnetic waves are an example that we will study later.

Types of wavesPulse wave: A wave that consists of a

single traveling pulse.Periodic wave: created by continuously

generated pulses from one end of the rope.

Types of wavesA wave whose source vibrates with

simple harmonic motion is a sine wave.

Types of wavesA transverse wave is a wave whose

particles vibrate perpendicularly to the direction the wave is traveling.

equilibrium

Wave CharacteristicsCrest: the highest point above the

equilibrium position.

Wave CharacteristicsTrough: the lowest point below the

equilibrium position.

Wave CharacteristicsWavelength: the distance between two

adjacent similar points of a wave◦crest to crest◦trough to trough

Wave CharacteristicsAmplitude: the maximum displacement

from equilibrium.◦Crest to equilibrium◦Trough to equilibrium

Types of wavesA longitudinal wave is a wave whose

particles vibrate in parallel to the direction the wave is traveling.

Types of waves

Wave characteristicsWave speed

Wave characteristicsWaves transfer energyThe rate of that transfer depends on the

amplitude at which the particles of the medium are vibrating.◦The greater the amplitude, the more energy

the wave carries.Damping occurs when that energy

diminishes over time.◦We disregard damping in many of our

problems.

Wave characteristicsThe energy transferred is proportional

to the square of the wave’s amplitude

Wave InterferenceTwo waves can occupy the same space

at the same time.The overlapping of two waves is called

superposition.

Wave InterferenceDisplacements in the same direction:

constructive interference.

Wave InterferenceDisplacements in opposite direction:

destructive interference.

Wave InterferenceWhat happens when waves hit a

boundary?◦Waves are reflected at a free boundary◦Waves are reflected and inverted at a fixed

boundary.

Wave InterferenceA standing wave is a wave pattern that

results when two waves of the same frequency, wavelength and amplitude travel in opposite directions and interfere.◦A node is a point in a standing wave that

maintains zero displacement.◦An antinode is a point in a standing wave

halfway between two notes at which the largest displacement occurs.

Sound Wave ProductionSound waves are longitudinal.Compression: the region of a

longitudinal wave in which the density and pressure are at a maximum.

Rarefaction: The region of a longitudinal wave in which the density and pressure are at a minimum.

Sound Wave ProductionSound waves are longitudinal because

vibrations of air molecules are parallel to the direction of wave motion.

Sound Wave ProductionTuning fork

Sound Wave ProductionTuning fork

Sound Wave CharacteristicsFrequency (cycles per second)◦Low frequency = long wavelength◦High frequency = short wavelength

Sound Wave CharacteristicsPitch: a measure of how high or low a

sound is perceived to be, depending on the frequency of the sound wave.

Sound Wave CharacteristicsSound can travel through solids, liquids

or gases.◦Waves consist of vibrating particles.◦Sound travels much more quickly through a

solid than a gas because the molecules are closer together.

Sound Wave Characteristics

Sound Wave CharacteristicsSound speed depends upon the

medium as we just saw. Sound speed also depends upon the

temperature of the medium.As temperature increases, gas particles

collide more frequently so sound can travel faster.

Temperature has a negligible effect on liquids or solids.

Sound Wave CharacteristicsSound waves propagate in three

dimensions.We assume a spherical wave front for

our purposes.

Wave fronts

** Distance between wave fronts equals one wavelength

Standing Waves on a string

Standing Waves on a string Fundamental frequency: the lowest

possible frequency of vibration of a standing wave.

Standing Waves on a string

These frequencies form the harmonic series.

Standing Waves on a string Harmonic series: a series of

frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency.

Standing Waves on a string Harmonic series of standing waves on

a vibrating string:

** Note: v is the speed of the waves on the string, not in the air.

Standing Waves in a pipeIf both ends of the pipe are open, all

harmonics are present.

v = the speed of sound in the pipeL = length of pipe

Standing Waves in a pipeIf one ends of the pipe is closed, only

odd harmonics are present.

v = the speed of sound in the pipeL = length of pipe

Standing Waves in a pipeBeat: the periodic variation in the

amplitude of a wave that is the superposition of two waves of slightsly different frequencies.

Standing Waves in a pipeThe number of beats per second

corresponds to the difference between frequencies.◦Two flute players could use beats to tune

their instrument. They would play the same note and one flute would be adjusted until no beats are heard, meaning the two flutes would be in tune.

Sound IntensityIntensity is the rate at which energy

flows through a unit area perpendicular to the direction of wave motion.

Sound IntensityIntensity of a spherical wave:

Sound IntensityIn combination, frequency and

intensity determine which sounds are audible.

Sound IntensityRelative intensity: the ratio of the

intensity of a given sound wave to the intensity at the threshold of hearing.

Sound IntensityThere is a logarithmic dependence of

perceived loudness on intensity.Loudness is measured according to a

decibel level.A decibel is a dimensionless unit that is

proportional to the log of a ratio using the threshold of hearing.

Sound IntensityIntensity (W/m2) Decibel Level (dB) Example

1.0x10-12 0 Threshold of hearing

1.0x10-11 10 Rustling leaves

1.0x10-10 20 Quiet whisper

1.0x10-9 30 Whisper

1.0x10-8 40 Mosquito buzzing

1.0x10-7 50 Normal conversation

1.0x10-6 60 Air conditioner at 6 m

1.0x10-5 70 Vacuum cleaner

1.0x10-4 80 Busy traffic

1.0x10-3 90 Lawn mower

1.0x10-1 110 Auto horn at 1 m

1.0x100 120 Threshold of pain

1.0x101 130 Machine gun

1.0x103 150 Jet plane

ResonanceNatural frequency: the frequency at

which a system tends to oscillate in the absence of any driving or damping force.

Resonance: a phenomena that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration.

ResonanceNatural frequency: the frequency at

which a system tends to oscillate in the absence of any driving or damping force.

Resonance: a phenomena that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration.