Sound and Waves

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Waves & Sound W. Sautter 2007

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The next slide is a quick promo for my books after which the presentation will begin Thanks for your patience! Walt S. Wsautter@optonline.net More stuff at: www.wsautter.com

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Books available at: www.wsautter.com www.smashwords.com www.amazon.com www.bibliotastic.com www.goodreads.com Walt’s Books for Free!

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Transverse waves (light) Longitudinal waves (sound) Types of Wave Motion These are also called Compressional Waves

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Crest Trough Compression Rarefaction Compression Compression Rarefaction Rarefaction Trough Crest Comparing Transverse & Longitudinal Waves Rarefaction = low Pressure Compression = high Pressure

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Wavelength λ Frequency ν Properties of Transverse Waves Velocity Wavelength λ Frequency ν Velocity v x =

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Wave A Wave A Wave A Wave B Wave B Wave B Constructive interference Destructive interference Partially Constructive interference Interference of Waves

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Sound Intensity Intensity = Power / Area Sound Source Sound radiates out from a source as concentric spheres and follows an Inverse Square function

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Sound Intensity 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 r 2 Power is measured in watts ( 1 joule / second) Intensity = Power / Area = watts/ 4 Π r 2 Or Watts / meter 2

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Decibels dB = 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 )

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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

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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 10 2 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

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Sound Intensity Whisper 20 decibels Plane 120 decibels Conversation 60 decibels Siren 100 decibels

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Tension, String Density & Frequency T _ m / L f = 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.

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The Doppler Effect 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) = - If source is moving towards the observer, V (source) = + f = f v + v _________ v + v observer observer source source air air + + ( (

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Slower at low temp Faster at high temp Speed of Sound Changes with Temperature

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V = 331.5 = .6 T 0 C Speed of Sound Changes with Temperature

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Doppler Effect ( moving source moving observer ) Moving Toward source Moving Toward observer Observed Frequency Is higher

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Doppler Effect ( moving source moving observer ) Moving Away from observer Moving Away from source Observed Frequency Is lower

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Doppler Effect ( moving source stationary observer ) Moving Away from observer Observer At rest Observed Frequency Is lower

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Doppler Effect ( moving source stationary observer ) Moving Toward observer Observer At rest Observed Frequency Is higher

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Open End Columns 1 / 2 λ 1 λ 3 / 2 λ Fundamental λ = 2 L Second Harmonic λ = L Third Harmonic λ = 2/3 L

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= 2 ( L + .8d ) λ fundamental Open End Columns λ fundamental ~ 2 L ~ d = diameter of tube L = length of tube at first resonant point If d is small compared to L (which is often true) then:

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

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Closed End Columns 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

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Closed End Columns = 4 ( L + .4 d ) λ fundamental λ fundamental ~ 4 L ~ d = diameter of tube L = length of tube at first resonant point If d is small compared to L (which is often true) then:

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Since V = λ f If velocity is constant then as 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 f = 5 f fund Fundamental f = f fund Second Harmonic f = 3 f fund Closed End Columns

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Waves in a String Fundamental λ = 2 L Second Harmonic λ = L Third Harmonic λ = 2 / 3 L Fourth Harmonic λ = ½ L Node Node VIBRATIONAL MODES

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Since V = λ f If velocity is constant then as λ decreases, f increases In the same ratio Second Harmonic λ = L Fundamental λ = 2 L Third Harmonic λ = 2/3 L Third Harmonic f = 3 f fund Fundamental f = f fund Second Harmonic f = 2 f fund Waves in a String

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

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