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 )

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

29. THE END