1. Mechanical Waves & Sound

2. Wave Motion
Waves are caused by

3. A vibration underneath the ocean can lead to a Tsunami

5. Wave anatomy:
Amplitude, A = Wavelength, λ =
Frequency, f = Period, T =
Wave velocity, v

6. Transverse and Longitudinal
Types of Waves:
Transverse and Longitudinal
Transverse
Longitudinal

7. Reflection of Waves

8. Reflection and Transmission of Waves
When wave enters NEW medium,

9. DIFFRACTION
Phenomena that occurs when an obstacle or opening causes wave to change direction and bend around it. 9

10. As the opening gets smaller, diffraction becomes more apparent.10

11. A swimmer is resting on a raft. He estimates that 3
A swimmer is resting on a raft. He estimates that 3.0m separates a trough and an adjacent crest of surface waves on the lake. He counts 14 crests that pass by the raft in 20.0 s. How fast are the waves moving?

12. REFRACTION 12

13. Wave slowing down…
Boundary between media
Why? 13

14. Wave Interference
When 2 or more waves overlap, they interfere (exist at same pt in space) to either add or subtract in amplitude 14

15. 2 Types of wave interference
1) CONSTRUCTIVE INTERFERENCE 15

16. 2) DESTRUCTIVE INTERFERENCE16

17. Destructive vs Constructive17

18. Speed of waves on string/wire
Speed of wave is determined by the tension and linear mass density of string 18

19. A wave moves at 24m/s when the wire is plucked. Mass of 3
A wave moves at 24m/s when the wire is plucked. Mass of 3.0kg hangs from the end of the string.
Find the mass per unit length of wire. 19

20. Standing Waves
String is plucked in middle sending waves in opposite directions
Waves reflect off wall travel back towards each other. 20

21. Standing Wave Pattern
If waves of the SAME FREQUENCY & AMPLITUDE interfere, a standing wave will emerge. 21

22. Standing Wave Modes
If a string is continually shaken at the right frequency you can establish standing waves.
n = 1
n = 2
n = 3
n = 4 22

23. Harmonics refer to the mode of the standing wave23

24. b) What is the fundamental frequency of vibration?
A standing wave is set up on a single string, as shown. The two fixed ends are attached to walls 73 cm apart.
a) If the string has a tension of 11.25N and linear mass density of 0.05kg/m, what is the frequency of the standing wave?
b) What is the fundamental frequency of vibration? 24

25. RESONANCE
Many objects have a natural frequency or fundamental mode they vibrate in if disturbed. 25

26. Sound waves are longitudinal
Sound waves REQUIRE a medium as do all mechanical waves. 26

27. Sound travels at different speeds in different materials
Sound travels at different speeds in different materials. Sound typically travels faster in a solid than in a liquid and faster in a liquid than a gas. 27

28. Speed of sound Speed of sound in AIR depends on temperature:
Room temperature is considered to be 20oC
Speed of sound in AIR depends on temperature: 28

29. Standing waves in air columns
Resonance can be achieved for sound waves as it was for strings.
This can occur for a pipe open at only one end or open at both ends.
This is the principle behind wind instruments. 29

30. Pipes open at both ends
Pipes open at each end are similar to strings and exhibit all-numbered harmonics where 30

31. Pipes closed at one end
Pipes closed at one end only exhibit odd-numbered harmonics where 31

32. Example: A flute is designed to play middle C (262 Hz) as the fundamental frequency when all the holes are covered at 20.0o C.
a) Approximately how long should the distance be from the mouthpiece to the end of the flute?
b) How far from the end (opposite mouthpiece) should the hole be that must be uncovered to play D above middle C, 294Hz?

33. Example: A piano string has length 1. 15m and mass 20g
Example: A piano string has length 1.15m and mass 20g. It is under tension of 6300N. If its fundamental sets an 0.98m long tube closed at one end into resonance at its 3rd harmonic, determine the temperature of the air.

34. Interference of waves & path length
Consider 2 point sources, S1 and S2 in phase. Together they create an interference pattern as shown based upon distance.

36. If we choose a different point B
The distance from S1 to B is
a distance of 3.5λ.
The distance from S2 to B is a distance of 5λ.

37. Antinodal Points: Nodal Points:
Formula for path length & interference (C.I. and D.I.)
Antinodal Points:
Nodal Points: S1 S2

38. Two speakers separated by a distance of 4
Two speakers separated by a distance of 4.30m emit sound of frequency 221Hz. The speakers are in phase with each other. A person listens from a location 2.80m directly in front of one of the speakers. Does person experience C.I. or D.I.? Assume room temperature.

39. A pair of in phase speakers are placed next to each other, 0.60m apart. You stand 1.0m directly in front of one of them. What is the lowest non-zero frequency that will produce constructive interference at your location? Assume room temperature.

40. DOPPLER SHIFT
Consider a stationary water spider doing pushups in a pool of water.
Circular waves travel outward in all directions at constant speed and wavelength at the frequency the spider is moving up and down. 40

41. Observers at points ‘A’ and ‘B’ would BOTH detect the SAME frequency of waves passing by them.
Spider is NOT moving
What IF spider starts to move across the water while still bobbing up and down…how will that change the waves produced?

42. If spider starts to move to the right while still making waves, then it looks like…
Note how waves get shorter on right side and longer on left side.

43. Observer ‘A’ detects LESS waves per second
Observer ‘A’ detects LESS waves per second. ‘B’ detects MORE waves per second.

44. Doppler formula

45. Applications of Doppler
Ultrasound (babies + blood flow in artery)
Weather radar
Police radar
Astronomy (blue shift vs red shift) for rotation, movement of stars, galaxies

46. Example
A car approaches at 25m/s sounding its horn while you stand on a corner. The horn sounds like 150Hz to you. Speed of sound is 343m/s. What is the actual frequency of the horn?

47. Beats
Beats result from interference between 2 waves of SIMILAR frequency
The waves demonstrate C.I. and D.I. periodically 47

48. Beats
Waves are in step at arrows 48

49. Example
A source emits a sound of wavelengths 3.15m and 3.50m in air at 20oC. How many beats per second will be heard?

50. Example
A guitar string is sounded with a 440Hz tuning fork, a beat frequency of 5Hz is heard. When the same string is sounded along with a 436Hz tuning fork, the beat frequency is 9Hz. What is the frequency of the string?

51. Sonic Boom Object moving at sonic speed, Mach 1
Object moving at subsonic speed
Object moving supersonic.

52. At the speed of sound (Mach 1), the vehicle is traveling fast enough to catch up with all of the forward moving sound waves, forming a strong pressure wave normal to the vehicle. This is the pressure wave that destroyed many aircraft before the flight of the X-1 in 1947.
If a moving source of sound moves at the same speed as sound, then the source will always be at the leading edge of the waves which it produces.

53. If the vehicle has the proper design and has enough power to exceed the speed of sound, it can out run the shock wave which then bends back to form a strong shock cone. When this cone reaches observers on the ground or at track side, the sudden change in pressure as the wave passes causes a sonic boom. Instead of these compressional regions (high pressure regions) reaching you one at a time in consecutive fashion, they all reach you at once.
As the vehicle passes through Mach 1 the pilot or driver senses a sudden silence because they are outrunning all air noise.

54. The circular lines represent compressional wavefronts of the sound waves. Notice that these circles are bunched up at the front of the aircraft. This phenomenon is known as a shock wave.