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Waves & Sound W. Sautter 2007
Transverse waves (light) Longitudinal waves (sound) Types of Wave Motion These are also called Compressional Waves
Comparing Transverse & Longitudinal Waves Rarefaction = low Pressure Compression = high Pressure Crest Trough Compression Rarefaction Compression Compression Rarefaction Rarefaction Trough Crest
Wavelength  Frequency    Properties of Transverse Waves Velocity Wavelength  Frequency    Velocity v x =
Constructive interference Destructive interference Partially Constructive interference Interference of Waves Wave A Wave A Wave A Wave B Wave B Wave B
Sound Intensity Intensity = Power / Area Sound Source Sound radiates out from a source as concentric spheres and follows an Inverse Square function
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
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 )
[object Object],[object Object],[object Object],[object Object],[object Object],Decibels are logarithmic functions
[object Object],[object Object],[object Object],[object Object],Decibels are logarithmic functions
Sound Intensity Whisper 20 decibels Plane 120 decibels Conversation 60 decibels Siren 100 decibels
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  =
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 + + ( (
Slower at low temp Faster at high temp Speed of Sound Changes with Temperature
Speed of Sound Changes with Temperature V  =  331.5  =  .6 T 0 C
Doppler Effect  ( moving source moving observer ) Moving  Toward source Moving  Toward observer Observed Frequency Is higher
Doppler Effect  ( moving source moving observer ) Moving  Away from observer Moving  Away from source Observed Frequency Is lower
Doppler Effect  ( moving source stationary observer ) Moving  Away from observer Observer At rest Observed Frequency Is lower
Doppler Effect  ( moving source stationary observer ) Moving  Toward observer Observer At rest Observed Frequency Is higher
Open End Columns 1 / 2   1    3 / 2   Fundamental     = 2 L Second Harmonic     =  L Third Harmonic     =  2/3 L
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 ~
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
Closed End Columns 1 / 4   3 / 4   5 / 4   Fundamental     = 4 L Second Harmonic     = 4/3 L Third Harmonic     =  4/5 L
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 ~
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
Waves in a String Fundamental     = 2 L Second Harmonic     =  L Third Harmonic     =  2 / 3  L Fourth Harmonic     =  ½ L Node Node VIBRATIONAL MODES
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
Waves from a Distant source = crest = trough Barrier with Two slits In phase waves Emerge from slits Constructive  interference Destructive interference Interference of  Waves
THE END

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Soundwaves 100212173149-phpapp02

  • 1. Waves & Sound W. Sautter 2007
  • 2. Transverse waves (light) Longitudinal waves (sound) Types of Wave Motion These are also called Compressional Waves
  • 3. Comparing Transverse & Longitudinal Waves Rarefaction = low Pressure Compression = high Pressure Crest Trough Compression Rarefaction Compression Compression Rarefaction Rarefaction Trough Crest
  • 4. Wavelength  Frequency  Properties of Transverse Waves Velocity Wavelength  Frequency  Velocity v x =
  • 5. Constructive interference Destructive interference Partially Constructive interference Interference of Waves Wave A Wave A Wave A Wave B Wave B Wave B
  • 6. Sound Intensity Intensity = Power / Area Sound Source Sound radiates out from a source as concentric spheres and follows an Inverse Square function
  • 7. 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
  • 8. 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 )
  • 9.
  • 10.
  • 11. Sound Intensity Whisper 20 decibels Plane 120 decibels Conversation 60 decibels Siren 100 decibels
  • 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 =
  • 13. 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 + + ( (
  • 14. Slower at low temp Faster at high temp Speed of Sound Changes with Temperature
  • 15. Speed of Sound Changes with Temperature V = 331.5 = .6 T 0 C
  • 16. Doppler Effect ( moving source moving observer ) Moving Toward source Moving Toward observer Observed Frequency Is higher
  • 17. Doppler Effect ( moving source moving observer ) Moving Away from observer Moving Away from source Observed Frequency Is lower
  • 18. Doppler Effect ( moving source stationary observer ) Moving Away from observer Observer At rest Observed Frequency Is lower
  • 19. Doppler Effect ( moving source stationary observer ) Moving Toward observer Observer At rest Observed Frequency Is higher
  • 20. Open End Columns 1 / 2  1  3 / 2  Fundamental  = 2 L Second Harmonic  = L Third Harmonic  = 2/3 L
  • 21. 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 ~
  • 22. 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
  • 23. Closed End Columns 1 / 4  3 / 4  5 / 4  Fundamental  = 4 L Second Harmonic  = 4/3 L Third Harmonic  = 4/5 L
  • 24. 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 ~
  • 25. 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
  • 26. Waves in a String Fundamental  = 2 L Second Harmonic  = L Third Harmonic  = 2 / 3 L Fourth Harmonic  = ½ L Node Node VIBRATIONAL MODES
  • 27. 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
  • 28. Waves from a Distant source = crest = trough Barrier with Two slits In phase waves Emerge from slits Constructive interference Destructive interference Interference of Waves