Sound, Wavefronts

Wavefronts join points in phase

Linear wavefronts

Wavefronts for compressional wave.

Rays – a ray is an arrow sketched through the wave fronts (perpendicular) to show direction of wave propagation.

Waves transfer energyEnergy is proportionalto the amplitude.

Less energy

More energy

For light increased amplitude increases brightness.

For sound: increased amplitude increases volume.

What does wave frequency (f) determine?

Wave type for EM waves.

Color for light.

Sound velocity solid

liquid

gas

In gas

hot faster.

cold slower.

Increasing velocity

The Doppler Effect

Stationary Source Emitting Waves all Directions. Circular wavefronts have = & f.

Doppler Effect from Moving Source

In front of source is less, behind is longer.

Another View

In front of source -short higher f:

hear higher pitch sound-see shorter light (blue).

behind source - longer lower f:

hear lower pitch soundsee longer light (red).

When objects are in relative motion:

a) Toward each other, f received increases.

b) Away from each other, f received decreases.

Doppler Effect

Resonance & Sympathetic Vibration

All objects have a naturalAll objects have a natural

frequency of vibration.frequency of vibration.

ResonanceResonance - the inducing- the inducingof vibrations of a naturalof vibrations of a naturalrate by a vibrating sourcerate by a vibrating source

having the same frequencyhaving the same frequency

““sympathetic vibrations”sympathetic vibrations”

Push at natural frequency, amplitude increases

Resonance:

An oscillatory system that is driven by a force with a frequency = to its natural frequency.

System will resonate – amplitude will increase.

Resonance & Sympathetic Vibration

Resonance occurs when a wave is in vicinity of an object & is vibrating at the natural frequency of the object. Object vibrates sympathetically at same frequency.

Continued vibration causes amplitude to increase.

mechanical universe resonance

A broad variety of tone colors exist because most sounds we perceive as pitch contain many frequencies.

• The predominant pitch The predominant pitch is called the is called the fundamental fundamental frequency. It is the frequency. It is the longest longest that forms a that forms a standing wave.standing wave.

Standing Wave patterns form notes.

Each string or pipe vibrates with particular frequencies of standing waves.

Other frequencies tend to die out.

Although we would perceive a string vibrating as a whole,

it vibrates in a pattern that appears erratic producing many different overtone pitches. What results are particular tone colors or timbres of instruments and voices.

Waveform with overtones.

Frequencies which occur along with the primary note are called the harmonic or overtone series.

When C is the fundamental the pitches below represent its first 15 overtones.

There are several standing waves which can be produced by vibrations on a string, or rope. Each pattern corresponds to vibrations which occur at a particular frequency and is known as a harmonic.

Harmonics

The lowest possible frequency at which a string could vibrate to form a standing wave pattern is known as the fundamental frequency or the first harmonic.

2nd Harmonic

Which One??

String Length L, & Harmonics

Standing waves can form on a string of length L, when the can = ½ L, or 2/2 L, or 3/2L etc.

Standing waves are the overtones or harmonics.

L = nn. n = 1, 2, 3, 4 harmonics. 2

Harmonic Frequencies

form where ½ can fit the string exactly.To calculate f:

L

nvf

2

f

vfv

2

nL

Substitute v/f for .

f

nvL

2

1st standing wave forms when = 2LFirst harmonic frequency is when n = 1 as below.

L

nvf

21

When n = 1 f is fundamental frequency or 1st harmonic.

L

nvf

22 For second harmonic n = 2.

f2 = v/L

Other standing waves with smaller wavelengths form other frequencies that ring out along with the fundamental.

In general,

The harmonic frequencies can be found where n = 1,2,3… and n corresponds to the harmonic. v is the velocity of the wave on the string. L is the string length.

L

nvfn 2

It is helpful to note that the distance between nodes on a standing wave is ½ .

½

Pipes and Air Columns

A resonant air column isA resonant air column issimply a standing simply a standing

longitudinallongitudinalwave system, much likewave system, much like

standing waves on a standing waves on a string.string. closed-pipe resonatorclosed-pipe resonator tube in which one end is tube in which one end is

openopenand the other end is closedand the other end is closed

open-pipe resonatoropen-pipe resonatortube in which both endstube in which both ends

are openare open

Open Pipe – open end has antinode.

Standing Waves in Open PipeBoth ends must be antinodes.

How much of the wavelength is the fundamental?

The 1st harmonic or fundamental can fit ½ into the tube.

Just like the string L = n 2

fn = nv2L

Where n, the harmonic is an integer.

Closed pipes must have a node at closed end and an antinode at the open end.

How many wavelengths??

Here is the next harmonic.How many ’s?

There are only odd harmonics possible.

L = 1/4.L = 3/4.L = 5/4

fn = nv where n = 1,3,5 … 4L

Beats – caused by constructive & destructive interference from 2

frequency sounds interacting.

• Beat Frequency heard is the difference between 2 frequencies.

• If a 50 Hz wave and a 60 Hz wave overlap, you hear beat of 10 Hz.

• hear beat frequencies

Traveling Waves Beats

Holt read 13 - 3

pg 509 38 - 39, 41, 44 46, 47 pg 499 #1 – 4

Start in class finish for hwk.