. 2 0 0 7W S a u t t e r

These are also calledCompressional Waves

Crest

Trough

Compression Rarefaction Compression CompressionRarefaction Rarefaction

Trough

Crest

Rarefaction = low PressureCompression = high Pressure

Wavelength

λ

Frequency

ν

Velocity Wavelength

λFrequency

ν Velocity

vx =

Wave A

Wave A

Wave A

Wave B

Wave B

Wave B

Constructive interference

Destructive interference

Partially Constructive interference

Intensity = Power / Area

SoundSource

Sound radiates out from a source as concentric spheresand follows an Inverse Square function

Inverse Square means as distance from the source doubles,the intensity 1/4 the original. If distance triples, the intensity

is 1/9 the original and so on.

The surface area of a sphere is given by 4 π r2

Power is measured in watts ( 1 joule / second)

Intensity = Power / Area = watts/ 4 π r2

Or Watts / meter2

dB = 10 log ( I / I0 )

I = the intensity of the sound to be evaluatedI0 = intensity of lowest sound that can be heard

(1 x 10-12 watts / meter2)

•SINCE LOGS ARE POWERS OF 10 THEY ARE USED JUST LIKE THE POWERS OF 10 ASSOCIATED WITH SCIENTIFIC NUMBERS.

•WHEN LOG VALUES ARE ADDED, THE NUMBERS THEY REPRESENT ARE MULTIPLIED.

•WHEN LOG VALUES ARE SUBTRACTED, THE NUMBERS THEY REPRESENT ARE DIVIDED

•WHEN LOGS ARE MULTIPLIED, THE NUMBERS THEY REPRESENT ARE RAISED TO POWERS

•WHEN LOGS ARE DIVIDED, THE ROOTS OF NUMBERS THEY REPRESENT ARE TAKEN.

Decibels are logarithmic functions

• A LOGARITHM (LOG) IS A POWER OF 10. IF A NUMBER IS WRITTEN AS 10X THEN ITS LOG IS X.

• FOR EXAMPLE 100 COULD BE WRITTEN AS 102 THEREFORE THE LOG OF 100 IS 2.

• IN PHYSICS CALCULATIONS OFTEN SMALL NUMBERS ARE USED LIKE .0001 OR 10-4. THE LOG OF .0001 IS THEREFORE –4.

• FOR NUMBERS THAT ARE NOT NICE EVEN POWERS OF 10 A CALCULATOR IS USED TO FIND THE LOG VALUE. FOR EXAMPLE THE LOG OF .00345 IS –2.46 AS DETERMINED BY THE CALCULATOR.

Decibels are logarithmic functions

Whisper 20 decibels Plane 120 decibels

Conversation 60 decibels Siren 100 decibels

The frequency of a string depends on the Tension (N)and string Linear Density in kilograms per meter (Kg/m).

Light strings under high tension yield high frequencies.Heavy strings under low tension yield low frequencies.

V (air) = 341 m/s at 20 oC

If observer is moving towards the source, V(observer) = +If observer is moving towards the source, V (observer) = -If source is moving towards the observer, V (source) = - If source is moving towards the observer, V (source) = +

Slower at low temp

Faster at high temp

0C

Moving Towardsource

Moving Towardobserver Observed Frequency

Is higher

Moving Away from

observer

Moving Away from

sourceObserved FrequencyIs lower

Moving Away from

observerObserver

At restObserved FrequencyIs lower

Moving Towardobserver

ObserverAt restObserved Frequency

Is higher

1/2 λ 1 λ 3/2 λ

Fundamental λ = 2 L Second Harmonic λ = L Third Harmonic λ = 2/3 L

λ fundamental

λ fundamental

d = diameter of tubeL = length of tube at first resonant point

If d is small compared to L(which is often true) then:

Since V = λ f

If velocity is constant thenas λ decreases, f increases

In the same ratio

Second Harmonic λ = L

Fundamental λ = 2 L

Third Harmonic λ = 2/3 L Third Harmonic λ =3 ffund

Fundamental f = ffund

Second Harmonic f = 2 ffund

1/4 λ 3/4 λ 5/4 λ

Fundamental λ = 4 L Second Harmonic λ = 4/3 L Third Harmonic λ = 4/5 L

λ fundamental

λ fundamental

d = diameter of tubeL = length of tube at first resonant point

If d is small compared to L(which is often true) then:

Since V = λ f

If velocity is constant thenas λ decreases, f increases

In the same ratio

Second Harmonic λ = 4/3 L

Fundamental λ = 4 L

Third Harmonic λ = 4/5 L Third Harmonic λ = 5 ffund

Fundamental f = ffund

Second Harmonic f = 3 ffund

Fundamental λ = 2 L

Second Harmonic λ = L

Third Harmonic λ = 2/3 L

Fourth Harmonic λ = ½ LNode

Node

VIBRATIONAL MODES

Since V = λ f

If velocity is constant thenas λ decreases, f increases

In the same ratio

Second Harmonic λ = L

Fundamental λ = 2 L

Third Harmonic λ = 2/3 L Third Harmonic λ = 3 ffund

Fundamental f = ffund

Second Harmonic f = 2 ffund

Waves from aDistant source = crest

= trough

Barrier withTwo slits

In phase wavesEmerge from slits

Constructive interference

Destructiveinterference