1. PowerPoint Lectures to accompany Physical Science, 8e Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 5 Wave Motions and Sound

2. Core Concept Sound is transmitted as increased and decreased pressure waves that carry energy.

3. Forces and Elastic Materials Elastic material Capable of recovering shape after deformation Rubber ball (elastic) versus lump of clay (inelastic) Spring forces 1.Applied force proportional to distance spring is compressed or stretchedproportional to 2.Internal restoring force arises, returning spring to original shape 3.Restoring force also proportional to stretched or compressed distance

4. Forces and Vibrations Vibration - repetitive back and forth motion Periodic motion - a motion that repeats itself When disturbed from equilibrium position, restoring force acts toward equilibrium Carried by inertia past equilibrium to other extreme Etc. Example of “simple harmonic motion” Simple harmonic motion: vibratory motion that occurs when there is a restoring net force opposite to & proportional to a displacement.

5. 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

6. Example 5.1 A vibrating system has a period of 0.5 s. What is the frequency in Hz? T=0.5s f= ?F=1/T = 1/0.5 s = 2/s = 2 Hz

7. Waves Periodic disturbances transporting energy Causes –Period motion disturbing surroundingsPeriod motion –Pulse disturbance of short durationPulse disturbance Mechanical waves –Require medium for propagation –Waves move through medium –Medium remains in place

8. 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 TroughCrest

9. 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

10. 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)

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

12. Sound Waves Require medium for transmission Speed varies with –Inertia of molecules –Interaction strength –Temperature Various speeds of sound Mediumm/sft/s Air (0°C)3311087 Hydrogen (0°C) 12844213 Water (25°C) 14974911 Lead19606430 Steel594019488

13. Waves in Air and Hearing 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 …

14. Velocity of Sound in Air Varies with temperature Greater kinetic energy  sound impulse transmitted faster Increase factor (units!): 0.6 m/s/°C; 2.0 ft/s/°C

15. Velocity of Sound in Air Speed of sounds at STP = 331 m/s Speed of sounds at 30° = 349 m/s

16. 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

17. 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)

18. 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

19. 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

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

21. Interference, cont. Destructive interference –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

22. Energy of Waves Intensity –Energy flowing (power) through a given area –Proportional to amplitude of sound wave, squared –Units = W/m 2

23. How loud is that sound? Subjective perception related to –Energy of vibrating object –Atmospheric conditions –Distance from source Intensity range of human hearing (decreases with age!)

24. Decibel Scale Better reflects nonlinear relationship between perceived loudness and intensity Logarithmic scale yields simpler numbers ExampleDecibelsIntensity (W/m 2 ) Threshold0 1  10 -12 Calm day10 1  10 -11 Whisper20 1  10 -10 Library40 1  10 -8 Talking65 3  10 -6 Heavy traffic70 1  10 -5 Pneumatic drill95 3  10 -3 Jet aircraft1201

25. 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

26. Sources of Sound Vibrating objects are the source of all sounds. Irregular, chaotic vibrations produce noise. Regular, controlled vibration can produce music. All sound is a combination of pure frequencies.

27. 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.

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

29. 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

30. 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 producedSupersonic speed