1. Wave Motions and Sound
Investigation 4

2. Forces and elastic materials
Capable of recovering shape after deformation
Rubber ball versus lump of clay
Spring forces
Applied force proportional to distance spring is compressed or stretched
Internal restoring force arises, returning spring to original shape
Restoring force also proportional to stretched or compressed distance

3. Forces and vibrations Vibration - repetitive back and forth motion
At the equilibrium position, spring is not compressed
When disturbed from equilibrium position, restoring force acts toward equilibrium
Carried by inertia past equilibrium to other extreme
Example of “simple harmonic motion”

4. Describing vibrations
Amplitude - maximum extent of displacement from equilibrium
Cycle - one complete vibration
Period - time for one cycle
Frequency - number of cycles per second (units = hertz, Hz)
Period and frequency inversely related

5. Waves Periodic (traveling) disturbances transporting energy Causes
Period motion disturbing surroundings
Pulse disturbance of short duration
Mechanical waves
Require medium for propagation
Waves move through medium
Medium remains in place

6. Kinds of waves Longitudinal waves
Vibration direction parallel to wave propagation direction
Particles in medium move closer together/farther apart
Example: sound waves
Gases and liquids - support only longitudinal waves

7. Kinds of waves, cont. Transverse waves
Vibration direction perpendicular to wave propagation direction
Example: plucked string
Solids - support both longitudinal and transverse waves
Surface water waves
Combination of both
Particle motion = circular

8. Waves in air Longitudinal waves only
Large scale - swinging door creates macroscopic currents
Small scale - tuning fork creates sound waves
Series of condensations (overpressures) and rarefactions (underpressures)

9. Hearing waves in air Range of human hearing: 20-20,000 Hz Infrasonic
Below 20 Hz
Felt more than heard
Ultrasonic
Dogs, cats, rats & bats
Used in imaging
Mechanism in ear
Eardrum, bones, fluid cell, hairs to nerve impulses…

10. Describing waves Graphical representation Wave terminology
Pure harmonic waves = sines or cosines
Wave terminology
Wavelength
Amplitude
Frequency
Period
Wave propagation speed

11. Sound waves Require medium for transmission Speed varies with
Inertia of molecules
Interaction strength
Temperature
Various speeds of sound

12. Velocity of sound in air
Varies with temperature
Warmer the air, greater the kinetic energy of the gas molecules
Molecules of warmer air transmit sound impulses from molecule to molecule more rapidly
Greater kinetic energy sound impulse transmitted faster
Increase factor (units!):
0.6 m/s/°C; 2.0 ft/s/°C

13. Visualization of waves
Sound = spherical wave moving out from source
Each crest = wave front
Wave motion traced with wave fronts
Far from source, wave front becomes planar

14. Refraction and reflection
Boundary effects
Reflection - wave bounces off boundary
Refraction - direction of wave front changes
Absorption - wave energy dissipated
Types of boundaries
Between different materials
Between regions of the same material under different conditions (temperature, pressure)

15. Refraction Bending of wave fronts upon encountering a boundary
Between two different media
Between different physical circumstances in the same medium
Example - temperature gradient in air

16. Reflection Wave rebounding off boundary surface
Reverberation - sound enhancement from mixing of original and reflected sound waves
Echo
Can be distinguished by human ear if time delay between original and reflected sound is greater then 0.1 s
Used in sonar and ultrasonic imaging

17. Interference Two or more waves combine Constructive interference
Peaks aligned with peaks; troughs aligned with troughs
Total wave enhanced

18. Interference, cont. Destructive interference Beats
Peaks aligned with troughs
Cancellation leads to diminished wave
Beats
Overall modulation of sound from mixing of two frequencies
Beat frequency = difference in two frequencies

19. Energy and sound Intensity Energy flowing (power) through a given area
Proportional to amplitude of sound wave, squared
Units = W/m2

20. Loudness Subjective perception related to
Energy of vibrating object
Atmospheric conditions
Distance from source
Intensity range of human hearing (decreases with age!)

21. Decibel scale
Better reflects nonlinear relationship between perceived loudness and intensity
Logarithmic scale means simpler numbers

22. Resonance
Excitation of natural frequency (“resonant frequency”) by a matching external driving frequency
Examples
Pushing a swing
Tuned boxes and tuning forks
Earthquake resistant architecture

23. Sources of sound Vibrating objects Source of all sound
Irregular, chaotic vibration produces noise
Regular, controlled vibration can produce music
All sound is a combination of pure frequencies

24. Vibrating strings Important concepts - strings with fixed ends
More than one wave can be present at the same time
Waves reflected and inverted at end points
Interference occurs between incoming and reflected waves

25. Vibrating strings, cont.
Standing waves
Produced by interferences at resonant frequencies
Nodes - destructive interference points
Anti-nodes - points of constructive interference

26. Resonant frequencies of strings
Fundamental - lowest frequency
Higher modes - overtones (first, second, …)
Mixture of fundamental and overtones produces “sound quality” of instrument
Formula for resonant frequencies

27. Sounds from moving sources
Doppler effect
Wave pattern changed by motion of source or observer
Approaching - shifted to higher frequency
Receding - shifted to lower frequency
Supersonic speed - shock wave and sonic boom produced

28. Problem1
A vibrating system has a period of 0.5s. What is the frequency in Hz?
For this problem all the ones to follow, answer on your own sheet of paper and show your work. Put your own name at the top although you may work as a team. Due today. 2 pts. Each.

29. Problem 2
A sound wave with a frequency of 260 Hz has a wavelength of 1.27m. With what speed would you expect this sound wave to move?

30. Problem 3
In general, the human ear is most sensitive to sounds at 2500 Hz. Assuming that sound moves at 330m/s, what is the wavelength of sounds to which people are most sensitive?

31. Problem 4
The human ear can distinguish a reflected sound pulse from the original sound pulse if 0.10s or more time elapses between two sounds. What is the minimum distance to a reflecting surface from which we can hear an echo if the speed of sound is 343 m/s?

32. Problem 5
A tuning fork vibrates times a second, producing sound waves with a wavelength of 78.0cm. What is the velocity of these waves?

33. Problem 6
The air temperature is 80deg F during a thunderstorm, and the thunder was timed 4.63s after lightning was seen. How many feet away was the lightning strike?

34. Problem 7
Why did the Apollo astronauts talk to each other while on the moon with radios? (Or, what we today would call cell phones)
How did they communicate with each other in the Lunar Module?

35. Problem 8
What is resonance?

36. Problem 9 What is the Doppler Effect?
Provide an example using sound waves.

37. Problem 10
During the days of the European Concorde airliner, people could experience sonic booms near the New York, London, and Paris airports: therefore, a not uncommon experience. Concorde no longer flies. What would you have to do, where would you go to experience one today?