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W. Sautter 2007
These are also calledCompressional Waves
Crest
Trough
Compression Rarefaction Compression CompressionRarefaction Rarefaction
Trough
Crest
Rarefaction = low PressureCompression = high Pressure
Wavelength
Frequency
Velocity Wavelength
Frequency
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 r2
Power is measured in watts ( 1 joule / second)
Intensity = Power / Area = watts/ 4 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 1 3/2
Fundamental = 2 L Second Harmonic = L Third Harmonic = 2/3 L
fundamental
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 = f
If velocity is constant thenas decreases, f increases
In the same ratio
Second Harmonic = L
Fundamental = 2 L
Third Harmonic = 2/3 L Third Harmonic =3 ffund
Fundamental f = ffund
Second Harmonic f = 2 ffund
1/4 3/4 5/4
Fundamental = 4 L Second Harmonic = 4/3 L Third Harmonic = 4/5 L
fundamental
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 = f
If velocity is constant thenas decreases, f increases
In the same ratio
Second Harmonic = 4/3 L
Fundamental = 4 L
Third Harmonic = 4/5 L Third Harmonic = 5 ffund
Fundamental f = ffund
Second Harmonic f = 3 ffund
Fundamental = 2 L
Second Harmonic = L
Third Harmonic = 2/3 L
Fourth Harmonic = ½ LNode
Node
VIBRATIONAL MODES
Since V = f
If velocity is constant thenas decreases, f increases
In the same ratio
Second Harmonic = L
Fundamental = 2 L
Third Harmonic = 2/3 L Third Harmonic = 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
