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 )
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
