4.
Wavelength Frequency Properties of Transverse Waves Velocity Wavelength Frequency Velocity v x =
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Constructive interference Destructive interference Partially Constructive interference Interference of Waves Wave A Wave A Wave A Wave B Wave B Wave B
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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 r 2 Power is measured in watts ( 1 joule / second) Intensity = Power / Area = watts/ 4 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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<ul><li>SINCE LOGS ARE POWERS OF 10 THEY ARE USED JUST LIKE THE POWERS OF 10 ASSOCIATED WITH SCIENTIFIC NUMBERS. </li></ul><ul><li>WHEN LOG VALUES ARE ADDED, THE NUMBERS THEY REPRESENT ARE MULTIPLIED. </li></ul><ul><li>WHEN LOG VALUES ARE SUBTRACTED, THE NUMBERS THEY REPRESENT ARE DIVIDED </li></ul><ul><li>WHEN LOGS ARE MULTIPLIED, THE NUMBERS THEY REPRESENT ARE RAISED TO POWERS </li></ul><ul><li>WHEN LOGS ARE DIVIDED, THE ROOTS OF NUMBERS THEY REPRESENT ARE TAKEN. </li></ul>Decibels are logarithmic functions
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<ul><li>A LOGARITHM (LOG) IS A POWER OF 10. IF A NUMBER IS WRITTEN AS 10 X THEN ITS LOG IS X. </li></ul><ul><li>FOR EXAMPLE 100 COULD BE WRITTEN AS 10 2 THEREFORE THE LOG OF 100 IS 2. </li></ul><ul><li>IN PHYSICS CALCULATIONS OFTEN SMALL NUMBERS ARE USED LIKE .0001 OR 10 -4 . THE LOG OF .0001 IS THEREFORE –4. </li></ul><ul><li>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. </li></ul>Decibels are logarithmic functions
12.
Tension, String Density & Frequency 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. T _ m / L f =
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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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Speed of Sound Changes with Temperature V = 331.5 = .6 T 0 C
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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 1 3 / 2 Fundamental = 2 L Second Harmonic = L Third Harmonic = 2/3 L
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Open End Columns d = diameter of tube L = length of tube at first resonant point If d is small compared to L (which is often true) then: = 2 ( L + .8d ) fundamental fundamental ~ 2 L ~
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Open End Columns Since V = f If velocity is constant then as decreases, f increases In the same ratio Second Harmonic = L Fundamental = 2 L Third Harmonic = 2/3 L Third Harmonic =3 f fund Fundamental f = f fund Second Harmonic f = 2 f fund
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Closed End Columns 1 / 4 3 / 4 5 / 4 Fundamental = 4 L Second Harmonic = 4/3 L Third Harmonic = 4/5 L
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Closed End Columns d = diameter of tube L = length of tube at first resonant point If d is small compared to L (which is often true) then: = 4 ( L + .4 d ) fundamental fundamental ~ 4 L ~
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Since V = f If velocity is constant then as decreases, f increases In the same ratio Second Harmonic = 4/3 L Fundamental = 4 L Third Harmonic = 4/5 L Third Harmonic = 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 = 2 L Second Harmonic = L Third Harmonic = 2 / 3 L Fourth Harmonic = ½ L Node Node VIBRATIONAL MODES
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Since V = f If velocity is constant then as decreases, f increases In the same ratio Second Harmonic = L Fundamental = 2 L Third Harmonic = 2/3 L Third Harmonic = 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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