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- 1. Introduction toWaves
- 2. What is a Wave?• Wave: motion of a disturbance– Disturbance creates waves thattravel away from the source of thedisturbance• Waves transport energy, not matter.• Mechanical waves require amedium: the elastic, deformablematter through which disturbancetravels• Electromagnetic waves don’trequire a medium
- 3. Waves Transport Energy not Matter
- 4. Types of Waves• Pulse Wave: source is anon-periodic disturbance• Periodic Wave: source isa periodic oscillation– If source is SHO, waveform is sine wave– Common forms:• Transverse• Longitudinal
- 5. Transverse Waves–Medium movesperpendicular to directionwave travels–Examples: Light, strings,seismic s-waves, waterwaves
- 6. Transverse Wave
- 7. Water Wave
- 8. Longitudinal Wave• Medium moves parallel todirection wave travels• Examples: sound, p-waves• Have compressions andrarefactions
- 9. Longitudinal Waves (cont.)• Additional terms with longitudinal waves:• Compression: where wave fronts arecloser together than in undisturbedmedium• Rarefaction: where they are farther apartthan in undisturbed medium
- 10. Longitudinal Pulse Wave
- 11. Representing a Longitudinal Waveas a Sine Wave
- 12. Wave ParametersThe following parameters are used todescribe waves:–Amplitude–Wave length–Frequency–Period–Speed
- 13. Amplitude (A)• How “tall” (or “wide”) the wave is• Maximum displacement from the averageor equilibrium position–Crests: highs–Troughs: lows–Measured from “crest to rest” or “troughto rest”• Unit of measure: meter
- 14. Amplitude and Energy
- 15. Amplitude (cont.)• These waves differ only in their amplitude:the “taller” wave has the greater amplitude• The amount of energy a wave transmits isrelated to its amplitude (proportional to A2)-3.0-2.0-1.00.01.02.03.00.0 5.0 10.0 15.0 20.0-3.0-2.0-1.00.01.02.03.00.0 5.0 10.0 15.0 20.0Amplitude = 2.0 cm Amplitude = 1.0 cmHow much more energy does the wave on theleft transmit? 4 times as much
- 16. Wave Length (λ)• Distance wave travels inone cycle• Distance from a point onone wave to the samepoint on the next wave–“Crest to crest,” “troughto trough” or any otherequivalent points onadjacent waves• Unit of measure: meterGraph of displacementversus distance is a“snapshot” of the wave ata given time
- 17. Parts of the Wave• Equilibrium – rest position, zero movement• Crest – top of wave• Trough – bottom of wave• Amplitude – height from rest to top or bottom• Wavelength – distance wave travels in 1 cycle
- 18. Frequency• Frequency: number of cycles (repetitions)per unit of time (how often wave cycles)• f = 1/T (T = period)• Units: Hz (cycles/second)
- 19. Frequency (cont.)• The higherfrequency wavehas morecomplete cyclesin the sameamount of timeGraph of displacement versus timeshows the motion of a given position
- 20. Period (T)• Time for one complete wave to pass anygiven point• Unit of measure: seconds• The period and frequency are reciprocals:T = 1/ff = 1/T
- 21. Wave Speed (v)• How fast a wave transmits energy fromone place to another• IMPORTANT: Wave speed depends onlyon specific properties of the medium)• For example:– Wave in string: tension and density– Wave in fluid: rigidity and density– Wave in solid: elasticity and density• Constant for a given medium at givenconditions• Changes only if properties of medium do!• Unit of measure: meter/sec
- 22. Wave Speed (cont.)• Wave speeds vary widely:–Water waves: a few miles per hour–Sound (in air): about 340 m/sec or 1100ft/sec (depends on temperature)–Electromagnetic waves (in vacuum): about3.0 x 108meters/sec or 186,000 miles/sec• Speed of light in a medium is alwayslower than that in vacuum
- 23. Wave Speed, Frequency, andWavelength are Related• These variables are related through thefollowing equation:speed (m/s) = frequency (Hz) x wavelength (m)• Better: the product of f and λ is v• CAUTION: Remember: wave speed doesn’tdepend on f or λ; it depends on. . .v = f λthe properties of the medium it’straveling through!
- 24. Practice Problem• What does each letter represent,assuming that the x-axis is position?• What if the x-axis is time?A = wavelength; C and E = wavelength/2;D = amplitude; B = 2 x amplitudeA = period; C and E = period/2;D = amplitude; B = 2 x amplitude
- 25. What is the wavelength?How could you find the amplitude?
- 26. Practice Problem• Between what points would you measureto find the wavelength?x, mAnswers: A to E; B to F; C to G
- 27. Wave Properties (cont.)• Here’s an example transverse waveshowing some of the quantities we’vetalked about so far:How many complete wavelengths are shown?x, m2

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