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# Waves Intro

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### Waves Intro

1. 1. Introduction to Waves
2. 2. What is a Wave? • Wave: motion of a disturbance – Disturbance creates waves that travel away from the source of the disturbance • Waves transport energy, not matter. • Mechanical waves require a medium: the elastic, deformable matter through which disturbance travels • Electromagnetic waves don’t require a medium
3. 3. Waves Transport Energy not Matter
4. 4. Types of Waves • Pulse Wave: source is a non-periodic disturbance • Periodic Wave: source is a periodic oscillation – If source is SHO, wave form is sine wave – Common forms: • Transverse • Longitudinal
5. 5. Transverse Waves –Medium moves perpendicular to direction wave travels –Examples: Light, strings, seismic s-waves, water waves
6. 6. Transverse Wave
7. 7. Water Wave
8. 8. Longitudinal Wave • Medium moves parallel to direction wave travels • Examples: sound, p-waves • Have compressions and rarefactions
9. 9. Longitudinal Waves (cont.) • Additional terms with longitudinal waves: • Compression: where wave fronts are closer together than in undisturbed medium • Rarefaction: where they are farther apart than in undisturbed medium
10. 10. Longitudinal Pulse Wave
11. 11. Representing a Longitudinal Wave as a Sine Wave
12. 12. Wave Parameters The following parameters are used to describe waves: –Amplitude –Wave length –Frequency –Period –Speed
13. 13. Amplitude (A) • How “tall” (or “wide”) the wave is • Maximum displacement from the average or equilibrium position –Crests: highs –Troughs: lows –Measured from “crest to rest” or “trough to rest” • Unit of measure: meter
14. 14. Amplitude and Energy
15. 15. Amplitude (cont.) • These waves differ only in their amplitude: the “taller” wave has the greater amplitude • The amount of energy a wave transmits is related to its amplitude (proportional to A2 ) -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 0.0 5.0 10.0 15.0 20.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 0.0 5.0 10.0 15.0 20.0 Amplitude = 2.0 cm Amplitude = 1.0 cm How much more energy does the wave on the left transmit? 4 times as much
16. 16. Wave Length (λ) • Distance wave travels in one cycle • Distance from a point on one wave to the same point on the next wave –“Crest to crest,” “trough to trough” or any other equivalent points on adjacent waves • Unit of measure: meter Graph of displacement versus distance is a “snapshot” of the wave at a given time
17. 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. 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. 19. Frequency (cont.) • The higher frequency wave has more complete cycles in the same amount of time Graph of displacement versus time shows the motion of a given position
20. 20. Period (T) • Time for one complete wave to pass any given point • Unit of measure: seconds • The period and frequency are reciprocals: T = 1/f f = 1/T
21. 21. Wave Speed (v) • How fast a wave transmits energy from one place to another • IMPORTANT: Wave speed depends only on 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 given conditions • Changes only if properties of medium do! • Unit of measure: meter/sec
22. 22. Wave Speed (cont.) • Wave speeds vary widely: –Water waves: a few miles per hour –Sound (in air): about 340 m/sec or 1100 ft/sec (depends on temperature) –Electromagnetic waves (in vacuum): about 3.0 x 108 meters/sec or 186,000 miles/sec • Speed of light in a medium is always lower than that in vacuum
23. 23. Wave Speed, Frequency, and Wavelength are Related • These variables are related through the following equation: speed (m/s) = frequency (Hz) x wavelength (m) • Better: the product of f and λ is v • CAUTION: Remember: wave speed doesn’t depend on f or λ; it depends on. . . v = f λ the properties of the medium it’s traveling through!
24. 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 amplitude A = period; C and E = period/2; D = amplitude; B = 2 x amplitude
25. 25. What is the wavelength? How could you find the amplitude?
26. 26. Practice Problem • Between what points would you measure to find the wavelength? x, m Answers: A to E; B to F; C to G
27. 27. Wave Properties (cont.) • Here’s an example transverse wave showing some of the quantities we’ve talked about so far: How many complete wavelengths are shown? x, m 2

Feb. 4, 2018
• #### FawwazGazh

Nov. 22, 2016
• #### mudassir94

Dec. 20, 2013

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