1. UNIT 5: VIBRATIONS, WAVES & SOUND

2. SIMPLE HARMONIC MOTION
Position vs. time graph for an object shows how oscillations can create waves.

3. UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND

4. WAVES Energy transfer can occur by doing work, by heat, or by waves!
Wave: a disturbance (vibration) that travels
mechanical waves require a material medium (solid, liquid, or gas) – particles vibrate in simple harmonic motion (water, sound, earthquake waves)
electromagnetic waves travel through a material or a vacuum – vibrating electric and magnetic fields (radio, microwave, infrared, visible light, ultraviolet, x-ray, gamma rays)

5. WAVES
Transverse waves: vibrations are perpendicular to wave direction

6. WAVES Longitudinal waves: vibrations parallel to wave direction
rarefaction

7. WAVES
Frequency, f: number of waves each second, unit: Hertz (Hz) Hz = 1 wave/sec
Period, T: time between identical points on two waves, unit: s f=1/T
Wavelength, l: distance between identical points on two waves, unit: m

8. WAVES Amplitude, A: maximum displacement from equilibrium, unit: m
Wave speed, v: speed of the wave, not the particles, unit: m/s v=fl
use difference in wave speeds to find distance
ex: lightning & thunder

9. WAVES
What could affect wave speed of a string being held tight between two points?
Wave speed is also proportional to tension and inversely proportional to μ (mass per unit length m/L)

10. UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND

11. WAVE INTERACTIONS
Each point on a wave travels in straight lines perpendicular to the wave front

12. WAVE INTERACTIONS
Reflection: waves "bounce back" at boundary

13. WAVE INTERACTIONS
Law of Reflection: qi = qr i: incidence, r: reflection

14. WAVE INTERACTIONS Reflection: with an open boundary
reflection is right-side-up

15. WAVE INTERACTIONS Reflection with a confined boundary
reflection is upside-down.

16. WAVE INTERACTIONS Absorption: wave energy becomes heat
Transmission: wave enters new medium, speed & l change

17. WAVE INTERACTIONS
Interference: waves pass through each other without changing each other, but their displacements add together

18. WAVE INTERACTIONS
constructive interference: combined wave displacement is greater than individual waves

19. WAVE INTERACTIONS
destructive interference: combined wave displacement is less than individual waves

20. Interference Condition for constructive interference:
D1 – D2 = n l where n = 1, 2, 3…
Condition for destructive interference:
D1 – D2 = (n+1/2) l where n = 0,1, 2, 3…
D1 is distance from first source to point
D2 is distance from second source to point

21. WAVE INTERACTIONS
Refraction: wave path bends as wave crosses boundary. Note that speed & wavelength change as wave moves into new medium, but frequency remains constant.

22. WAVE INTERACTIONS
Refraction: wave bends toward the normal when it slows down

23. WAVE INTERACTIONS
Refraction: wave bends away from the normal when it speeds up

24. WAVE INTERACTIONS
Diffraction wave spreads out or “bends” beyond edge of barrier

25. WAVE INTERACTIONS
Diffraction greatest when l is greater than or equal to the size of opening or object

26. WAVE INTERACTIONS
Standing Waves: interference of two identical waves going opposite directions makes waves appear to vibrate in place

27. WAVE INTERACTIONS Standing Waves: nodes: no displacement
loops or antinodes: maximum displacement
node distance = l/2

28. SOUND WAVES
Source: a vibrating object (vocal cord, string, reed, etc.)

29. SOUND WAVES
Wave type:
mechanical
longitudinal
graph as transverse

30. SOUND WAVES Pitch: musical tone or note – frequency of a wave
sonic spectrum:
musical scale: specific proportional frequencies
C major scale C D E F G A B
frequency (Hz)
264
297
330
352
396
440
495
528

31. MUSICAL INSTRUMENTS Stringed Instruments
string pitch = resonant vibrating frequency of string
fundamental (lowest f): string is a single loop standing wave
harmonic: integer multiple of fundamental

32. MUSICAL INSTRUMENTS l=2L/n L: length of string, and n is 1,2,3…
f=v/l v: wave speed in string
v=√TL/m T: tension, m: mass of string

33. MUSICAL INSTRUMENTS Stringed Instruments
quality: mixture of fundamental and harmonics (makes different instruments sound different)
sound boards & boxes: more air surface contact - amplifiers

34. MUSICAL INSTRUMENTS

35. MUSICAL INSTRUMENTS Wind Instruments
pitch = frequency of vibration of column of air
f = v/l v: sound speed in air l: wavelength, depends on length of air column

36. MUSICAL INSTRUMENTS open-end tube: each end of tube is antinode
l = 2L/n L: length of tube and n is 1,2,3…
Examples: flutes, saxophones, some organ pipes

37. MUSICAL INSTRUMENTS closed-end tube: closed end of tube is node
l=4L/n L: length of tube and n is 1,3,5
Examples: clarinets, some pipe organs

38. UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND

39. SOUND INTERACTIONS
Echo: sound wave reflection; maximum from rigid, smooth surfaces
sonar: distance by timing pulse echoes, x = vsoundt (repeated echoes give a "picture" of surface)
ultrasound: sonar using 1-10 MHz waves (detects smaller objects, inaudible); body vsound = 1540 m/s

40. SOUND INTERACTIONS Resonance (sympathetic vibration)
objects have natural vibrating frequency
sending waves to an object at at its natural frequency will make it vibrate
pushing a child on a swing
using microwaves to heat up water

41. SOUND INTERACTIONS

42. SOUND INTERACTIONS
The Doppler Effect: apparent change in frequency due to motion of source or listener

43. SOUND INTERACTIONS The Doppler Effect Source is moving toward observer
Observer is moving toward the source
Vs = speed of source
fo = observed frequency
fs = frequency of source
V0 = speed of observer
C = wave speed

44. SOUND INTERACTIONS The Doppler Effect
Source is moving away
Vs = speed of source
fo = observed frequency
fs = frequency of source
V0 = speed of observer
C = wave speed
Observer moving away from the source

45. Doppler Effect What if both source and observer are moving?
If observer and source are moving toward each other then (+/-)
If observer and source are moving away from each other then (-/+)
Vs = speed of source
fo = observed frequency
fs = frequency of source
V0 = speed of observer
C = wave speed

46. SOUND INTERACTIONS
Radar: uses Doppler Effect in radio waves reflected off an object to determine its speed
Red shift and Blue shift of light tells astronomers whether a star is moving toward or away from Earth.

47. SOUND INTERACTIONS

48. SOUND INTERACTIONS The Doppler Effect
sound barrier: “pile-up” of sound waves (pressure) in front of object traveling Mach 1
sonic boom: cone-shaped pressure pulse following an object traveling at supersonic speeds (water wake following a speedboat)

49. SOUND INTERACTIONS

50. UNIT 5: VIBRATIONS, WAVES & SOUND
PHYSICS
UNIT 5: VIBRATIONS, WAVES & SOUND

51. QUIZ 5.4
The speed of sound in earth is 3500 m/s. An earthquake wave, frequency 5 Hz, travels from its source to a distant mountain range and returns in 3.4 minutes.
(a) How far away is the mountain range?
(b) What is the wavelength of the earthquake wave?
(c) If the mountain range was moving away at 0.50 m/s. what would be the frequency of the reflected wave?
357,000 m
700 m
5.00 Hz

52. UNIT 5 REVIEW f = 1/T v = fl qi = qr visinqr = vrsinqi node dist = l/2
loop height = 4A
v = T
I = P/4pr2
b = 10log(I/I0)
I0 = 1×
10-12 W/m2
open pipe l = 2L
closed pipe l = 4L
x = vt