Waves Intro
- 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. Waves Transport Energy not Matter
- 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. Transverse Waves –Medium moves perpendicular to direction wave travels –Examples: Light, strings, seismic s-waves, water waves
- 7. Water Wave
- 8. Longitudinal Wave • Medium moves parallel to direction wave travels • Examples: sound, p-waves • Have compressions and rarefactions
- 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
- 11. Representing a Longitudinal Wave as a Sine Wave
- 13. Wave Parameters The following parameters are used to describe waves: –Amplitude –Wave length –Frequency –Period –Speed
- 14. 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
- 16. 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
- 17. 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
- 18. 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
- 19. Frequency • Frequency: number of cycles (repetitions) per unit of time (how often wave cycles) • f = 1/T (T = period) • Units: Hz (cycles/second)
- 20. 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
- 21. 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
- 22. 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
- 23. 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
- 24. 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!
- 25. 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
- 26. What is the wavelength? How could you find the amplitude?
- 27. Practice Problem • Between what points would you measure to find the wavelength? x, m Answers: A to E; B to F; C to G
- 28. 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
Editor's Notes
- #2: Resources: The Physics Classroom, Daniel A. Russell
- #17: How much more energy per unit time does the wave on the left transmit? Since its amplitude is twice as large, it transmits 4 times the energy
- #21: The upper wave has 2 x the frequency of the bottom. Note that the x-axis has units of time in this graph.
- #23: Examples: Speed of wave in string depends on tension and linear density. Speed of wave in fluid depends on bulk modulus and density. Speed of wave in solid depends on elastic modulus and density.
- #25: Recall that speed v = distance traveled/time, or v = wavelength/period = wavelength x frequency
- #29: Answer: 2 complete wavelengths are shown