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 dontrequire 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 WavesMedium movesperpendicular to directionwave travelsExamples: 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:AmplitudeWave lengthFrequencyPeriodSpeed 13. Amplitude (A) How tall (or wide) the wave is Maximum displacement from the averageor equilibrium positionCrests: highsTroughs: lowsMeasured 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 () Distance wave travels inone cycle Distance from a point onone wave to the samepoint on the next waveCrest to crest, troughto trough or any otherequivalent points onadjacent waves Unit of measure: meterGraph of displacementversus distance is asnapshot 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 hourSound (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 is v CAUTION: Remember: wave speed doesntdepend on f or ; it depends on. . .v = f the properties of the medium itstraveling 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.) Heres an example transverse waveshowing some of the quantities wevetalked about so far:How many complete wavelengths are shown?x, m2