WAVES AND SOUND

Animations courtesy of Dr. Dan Russell, Kettering University

SIMPLE HARMONIC MOTION

At rest, the mass is at its equilibrium position

If displaced and released from the equilibrium position, it will vibrate about the equilibrium position

This is known as simple harmonic motion

Any object vibrating about an equilibrium position is undergoing simple harmonic motion

DESCRIBING HARMONIC MOTION Amplitude (A) – maximum

displacement from equilibrium (units: meters)

Period (T) – amount of time elapsed after 1 complete vibration (or cycle) (units: seconds)

Frequency (f) – how many cycles completed in 1 second (units: cycles/ second or Hertz)

THE MATHEMATICAL RELATIONSHIP BETWEEN PERIOD AND FREQUENCY

They are inverse quantities

f = 1 / T (Hz)

T = 1 / f (s)

WAVES Waves are generated by harmonic

motion

Waves require a medium to travel throughA medium is any solid, liquid, or gas

Waves represent the transfer of energy through a medium

Wave pulse animation

LONGITUDINAL AND TRANSVERSE WAVES

When a waves travel through a medium, the particles of the medium vibrate

Longitudinal wave – particles of the medium vibrate parallel to the direction that the wave is traveling

Transverse wave – particles of the medium vibrate perpendicular to the direction that the wave is traveling

Wave animations

DESCRIBING WAVES Since harmonic motion generates waves,

the same terms are used to describe both Amplitude – height of the wave (units:

meters) Frequency – how many waves pass you

each second (units: waves per second or Hertz)

Period – amount of time that elapses between each successive wave (units: seconds)

Wavelength – distance between waves (units: meters)

DESCRIBING WAVES

THE VELOCITY OF A WAVE Velocity of a wave = wavelength x

frequency (units: m/s) This equation applies to all waves

v = λ f

SOUNDSound waves are longitudinal

waves

The speed of sound depends on the air temperature

It increases by 0.6 m/s for each degree Celsius above 0 oC

THE SPEED OF SOUND The formula for the speed of sound at a

certain air temperature:

S = 331m/s + (0.6m/s/oC)T

S = speed of sound T = temperature This formula is accurate between 0-100oC

WAVEFRONTS Sound waves spread from their source

as spherical waves

Each successive wave is called a wavefront

Animation

WAVEFRONTS BECOME LINEAR FAR FROM THE SOURCE

REFLECTION When a wavefront encounters a

boundary between two mediums, reflection occurs

An echo is an example of sound being reflected

SONAR uses reflection of waves to locate objects under water

Part of the wave is transmitted to the other medium

REFRACTIONRefraction – when a wave changes

direction Causes:

A wave travels from one medium into anotherEx: Sound traveling from air into water

When a wave encounters different conditions within a mediumEx: Sound traveling into air of a different temperature

REFRACTIONThe direction of the wavefront changes because of

the temperature difference in the air

REFRACTIONRefraction animation

THE PRINCIPLE OF SUPERPOSITION: INTERFERENCE

When two waves cross, another wave is created which is the sum of the two individual waves

Interference animation

This is known as the principle of superposition

The Principle of Superposition results in what is called interference

There are two types of interference: Constructive Destructive

CONSTRUCTIVE INTERFERENCE

DESTRUCTIVE INTERFERENCE

BEAT FREQUENCIES Imagine 2 sources generating waves of

slightly different frequencies

Interference will cause what is known as a beat frequency

The beat frequency equals the difference between the source frequencies

fb = f2 – f1

BEAT FREQUENCIES

VIBRATING STRINGS AND STANDING WAVES When a transverse wave reaches a

boundary, the reflected wave is inverted

Reflection animation

Reflected waves interfering with incoming waves of the same frequency produce standing waves

Standing wave animation Standing wave animation 2

THE SPEED OF A WAVE ON A STRING

The speed of a wave on a string depends on the tension of the string, and the mass per unit length of the string

It is given by the following formula:

RESONANCE All material objects have a natural

frequencies of vibration (harmonic frequencies)

When the frequency of an applied force on an object matches a harmonic frequency, energy is transferred very efficiently

This is known as resonance During resonance, the amplitude of

vibration becomes very high The harmonic frequencies of a vibrating

string and an open tube are examples of resonance and are also called resonant frequencies

VIDEOS Wine Glass Tacoma Narrows bridge

HARMONICS Consider a string tied down at both

ends

It will only vibrate at certain frequencies The resonant or natural frequencies of

vibration

These are also known as harmonic frequencies

THE FUNDAMENTAL FREQUENCY OF A VIBRATING STRING

The string will also vibrate at frequencies that are integer multiples of the fundamental frequency

These are known as Harmonic frequencies Harmonic frequencies produce standing waves

THE DOPPLER EFFECT The frequency of a sound wave will

change if the source of the sound is moving relative to you

If the source is moving towards you, the frequency increases

If the source is moving away from you, the frequency decreases

This is known as the Doppler effect

STATIONARY SOURCE

MOVING SOURCE

VIDEOS Listener in motion

Car horn

INTERFERENCE AND STANDING WAVES http://www.youtube.com/watch?v=tI6S5CS-6J

I&NR=1 Water

http://www.youtube.com/watch?v=LCk9-blM5Xg&feature=related Cornstarch

http://www.youtube.com/watch?v=4shodbQMcmM&NR=1 Faraday waves

http://www.youtube.com/watch?v=Yw4qklgNIxI&feature=related Speakers

http://www.youtube.com/watch?v=nO0bSSXmr1A rice

BREECHING THE SOUND BARRIER