sound. loudness and pitch frequency = pitch amplitude = volume or intensity i a 2. if a doubles i...

Sound

Loudness and Pitch

• frequency = pitch

• Amplitude = volume or intensity

• I A2.

• If A doubles I increase by 22 or 4.

Standing Wave & Resonance

pattern that results when 2 waves, of same f, & A travel in opposite directions.

Often formed from pulses reflect off a boundary. Waves interfere constructively (antinodes) & destructively (nodes) at fixed points.

Standing waves have no net transfer of energy – no direction propagation of energy.

Standing Waves form at natural frequencies of the material. Occur when material is at resonance.

When system is disturbed it vibrates at many frequencies. Standing wave patterns continue. Other frequencies to die out.

Since there is resonance, the amplitude of particular wavelengths/frequencies will be amplified.

Relation of Wavelength to String Length for Standing Waves L = 1/2.

= L.

= L

General expression relating wavelength to string length for standing waves:

• n ( ½ ) = L

• n is a whole number

• A whole number of half ’s must fit.

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.

Each standing wave pattern on a string can produce 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 whole number harmonics. 2

FrequenciesSince standing wave forms where ½ can fit the string exactly, we can calculate f:

L

nvf

2

f

vfv

2

nL

Substitute v/f for .

f

nvL

2

Must know speed in material.

n = harmonic

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

L

nvf

21

When n = 1, f = v/ . This is fundamental frequency or 1st harmonic.First harmonic has largest amplitude.

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

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

Pipes – the 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 Pipe Resonator

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

How many wavelengths? L = 4

Here is the next harmonic.How many ’s?

L = 34

There are only odd harmonics possible – n = odd number only.

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

fn = nv where n = 1,3,5 … 4L

Application: When waves propagate through a tall building, the building resonates like a tube open at two ends.

• What is the equation that relates frequency to wave velocity and building height?

L

nvf

21

The building is 360 m tall and allows waves to travel through it at 2400 m/s, what frequency wave will cause the most damage to it? Explain why.(Hint: What is the resonant frequency)?

• 3.3 Hz

Holt read 13 - 3

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

Start in class finish for hwk.

Hwk read 491 – 503

do 499 and 503