W Sautter 2007 These are also called Compressional

W. Sautter 2007

These are also called Compressional Waves

Crest Trough Compression Trough Rarefaction Compression = high Pressure Rarefaction = low Pressure

Frequency Wavelength Velocity Wavelength Frequency Velocity = x v

Wave B Wave A Constructive interference Wave A Wave B Destructive interference Wave B Wave A Partially Constructive interference

Intensity = Power / Area Sound Source Sound radiates out from a source as concentric spheres and 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 r 2 Power is measured in watts ( 1 joule / second) Intensity = Power / Area = watts/ 4 r 2 Or Watts / meter 2

d. B = 10 log ( I / I 0 ) I = the intensity of the sound to be evaluated I 0 = intensity of lowest sound that can be heard (1 x 10 -12 watts / meter 2)

Decibels are logarithmic functions • 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 10 X 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.

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 o. C 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) = +

at r e t Fas Slo we ra t lo wt em h p m e t igh p

0 C

Moving Toward observer Observed Frequency Is higher Moving Toward source

Moving Away from observer Observed Frequency Is lower Moving Away from source

Moving Away from observer Observed Frequency Is lower Observer At rest

Moving Toward observer Observed Frequency Is higher Observer At rest

3/2 1 Fundamental = 2 L Second Harmonic = L Third Harmonic = 2/3 L

fundamental d = diameter of tube L = length of tube at first resonant point If d is small compared to L (which is often true) then: fundamental

Since V= f If velocity is constant then as decreases, f increases In the same ratio Fundamental = 2 L Fundamental f = ffund Second Harmonic = L Second Harmonic f = 2 ffund Third Harmonic = 2/3 L Third Harmonic =3 ffund

1/4 Fundamental = 4 L 3/4 5/4 Second Harmonic = 4/3 L Third Harmonic = 4/5 L

fundamental d = diameter of tube L = length of tube at first resonant point If d is small compared to L (which is often true) then: fundamental

Since V= f If velocity is constant then as decreases, f increases In the same ratio Fundamental = 4 L Fundamental f = ffund Second Harmonic = 4/3 L Second Harmonic f = 3 ffund Third Harmonic = 4/5 L Third Harmonic = 5 ffund

Node Fundamental = 2 L Second Harmonic = L Third Harmonic = 2/3 L Node Fourth Harmonic = ½ L VIBRATIONAL MODES

Since V= f If velocity is constant then as decreases, f increases In the same ratio Fundamental = 2 L Fundamental f = ffund Second Harmonic = L Second Harmonic f = 2 ffund Third Harmonic = 2/3 L Third Harmonic = 3 ffund

Destructive interference Waves from a Distant source = crest = trough Constructive interference Barrier with Two slits In phase waves Emerge from slits