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Waves Review

Waves Review. Ch13 (p408-433) Ch14(all). Overview. Waves are created when a periodic disturbance propagates outwards, transmitting energy (but not matter). Five wave properties: Speed (v, m/s): Determined by the elastic and inertial properties of the medium. v=d/t v= l f= l /T

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Waves Review

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  1. Waves Review Ch13 (p408-433) Ch14(all)

  2. Overview Waves are created when a periodic disturbance propagates outwards, transmitting energy (but not matter). Five wave properties: • Speed (v, m/s): Determined by the elastic and inertial properties of the medium. v=d/t v=lf=l/T • Frequency (f, Hz): Cycles per second. Determined by the oscillating source of the wave. • Period (T, s): Seconds per cycle. How much time ti takes for wave motion to repeat. The reciprocal of frequency. • Wavelength (l, m): Distance between two identical points on a wave. (eg. From crest to crest). • Amplitude: Size of wave disturbance. Half the distance from peak to crest. Classifications (recognize and give examples of each) Mechanical vs. Electromagnetic Pulsed vs. Continuous Transverse vs. Longitudinal Traveling vs. Standing

  3. Oscillators Springs: |Fsp|=|kx| Usp= ½ kx2 T=2p(m/k)½ Energy is conserved so: ½ kx2 + ½ mv2 = constant = ½ kA2 Pendulums: T=2p(L/g)½

  4. Change of direction Reflection: Incident wave bounces back from interface (qincident=qreflection) Diffraction: Wave curves around a barrier or spreads out when passing through an opening (no change of medium) Refraction: Incident wave is bent as it is transmitted across an interface (Snell’s Law)

  5. Wave interference Law of superposition: when two waves coincide their amplitudes are added Constructive interference: when two waves are “in sync” their amplitudes combine Destructive interference: when crests of one wave coincide with troughs of other they cancel out Examples: • Standing waves and resonance • Beats • Double slit interference • Single slit diffraction • Thin film interference

  6. Standing waves • String fixed on each end, or tube open on each end: l1 = 2L, ln=l1/n n=1,2,3,4,…. f1 = v/2L fn=nf1 • Tube closed on one end l1 = 4L ln=l1/n n=1,3,5,7…. f1=v/4L fn=nf1

  7. Beats When waves of slightly different frequency go in and out of sync they cycle between constructive and destructive interference which results in a periodic variation in their amplitude Fbeat=|f1-f2|

  8. Double slit interference Requirements: • Incident waves should be monochromatic (single wavelength) & coherent (arrive at each slit “in sync”) • Slits should be small enough to cause waves to diffract (and spread out) • Different path lengths mean that waves arriving from each slit may or may not be in sync. Condition for constructive interference: Dx=nl (n=1,2,3…) Double slit interference results in constructive interference when: dsinq=nl or yn=nlL/d Single slit diffraction results in destructive interference when: asinq=nl or yn=nlL/a Bragg scattering (x-rays!) results in constructive interference when: 2dsinq=nl

  9. Doppler effect When source and observer are in relative motion toward one another the wavelength is decreased, and the frequency is increased (ambulance approaching) When source and observer are in relative motion away from one another the wavelength is increased, and the frequency in decreased (ambulance receding) For sound waves this caused the PITCH to shift up (toward) or down (away). For light (EM) waves this causes the COLOR to shift blue (toward) or red (away) Doppler has nothing to do with amplitude and what matters is relative motion NOT proximity f’ = f (v+vo)/(v-vs) for motion toward (reverse signs for motion apart

  10. A wave that requires a physical medium to travel through Mechanical wave

  11. Explain what each symbol in the formula yn=nlL/d stands for and when this formula might be used Formula used for double slit interference when the screen is far (L>>d from the slits) l=wavelength d=distance between the openings L=distance from the slits to the screen Yn=distance on screen to interference peek n=an integer

  12. Because particles of air move back in forth in the direction that a sound wave is travelling, sound must be a _______. Longitudinal wave

  13. Wave property that depends on the medium the wave is traveling through. Wave speed

  14. The change in pitch heard as an ice cream truck approaches and then recedes is an example of ______. The Doppler Effect

  15. A wave that requires a physical medium to travel through Mechanical wave

  16. The ______ of a wave does not change as it enters a new medium. A) Speed C) direction B) Wavelength D) frequency D) frequency

  17. The formula for spring potential energy is: U=½kx2

  18. The bending of a wave as it enters a new medium is called______: Refraction

  19. A wave that completes 30 oscillations in one minute has a period of ___ s, a frequency of ____ Hz. 2.0 seconds, 0.5 Hz

  20. A sound wave traveling at a speed of 340 m/s has a wavelength of 1.7 meters. What is its frequency? 200 Hz

  21. A 42.5 cm long tube is open on both ends. What is the fundamental resonant frequency if the speed of sound is 340 m/s? What are the next two harmonics for this tube? f1=v/2L=340/0.85=400Hz f2=2f1=800 Hz, f3=1200 hz

  22. An astrophysicist observes a distant galaxy moving away from us. Due to the galaxy’s motion its light would: a) Shift toward red end of spectrum b) Shift toward blue end of spectrum c) Take longer to reach us d) Have a longer wavelength and a smaller frequency. Both a and d are correct!!

  23. A 1.2 meter long organ pipe is closed on one end. Its fundamental frequency is 72.9 Hz. Determine the next two harmonics, and the speed of sound. f3=3f1=219 Hz f5=365Hz l1=4L=4.8m v=l1f1=350 m/s

  24. The period of spring oscillation is given by the formula: T=2p(m/k)½

  25. The period of oscillation for a simple pendulum is given by the formula: T=2p(L/g)½

  26. A 2.0 kg mass hanging from a spring is in static equilibrium when the spring stretches by 80 cm. What is the spring constant? Fsp – Fg = 0 kx = mg k = mg/x = 20/.8 = 25 N/m

  27. List the parts of the electromagnetic spectrum from longest wavelength to shortest. Radio,micro,IR,VIS,UV,x-ray, gamma

  28. What is the speed of a radio wave? 3x108m/s (same for all EM waves in air or vacuum)

  29. 400 nm light strikes two narrow slits that are separated by 0.40 mm. A screen is located 2.0 meters away. How far apart will the bright lines be located? How would their separation change if the slits were further apart? Yn=nlL/d Y1=4x10-7x2/4x10-4=2mm (since this is the distance from central maximum we have answered the question) There is an inverse relation between yn and d, so moving the slits further would make the bright lines closer to one another)

  30. A 3.0 kg bob oscillates 40 times per minute at the end of string. How long is the string? F=40/60=2/3 hz T=1/f=1.5 s T=2p(L/g)1/2 L=(gT2)/(4p2)= 57 cm

  31. A plucked guitar string is an example of a… (standing/traveling), (transverse/longitudinal), (mechanical/EM) wave Standing, transverse, mechanical

  32. A wave that does not require a physical medium to travel through is an ______ wave. Electromagnetic wave

  33. The boundary between two media is called an ______. interface

  34. Write the formula for the Doppler effect and explain what each term means. f’=f(v+vo)/(v-vs) f=original frequency of the sound v=speed of the sound vo = speed of the observer (relative to the air) vs = speed of the source (relative to the air) f’ = the doppler shifted frequency heard by the observer Algebraic signs given are for relative motion toward one another

  35. A stereo is blasting a 660 Hz pitch from a car that is traveling away from you at 20 m/s. (use vsound = 343 m/s) • Is the pitch you hear higher or lower than that heard by the person in the car? • What is the frequency of the sound that you detect? Pitch is LOWER. f’=f(v+vo)/(v-vs)=660(343)/(363)=624 Hz Note the change of sign…using the negative would have given us a HIGHER pitch which is WRONG!!

  36. A wave that requires a physical medium to travel through Mechanical wave

  37. A wave that requires a physical medium to travel through Mechanical wave

  38. A wave that requires a physical medium to travel through Mechanical wave

  39. A wave that requires a physical medium to travel through Mechanical wave

  40. A wave that requires a physical medium to travel through Mechanical wave

  41. A wave that requires a physical medium to travel through Mechanical wave

  42. A wave that requires a physical medium to travel through Mechanical wave

  43. A wave that requires a physical medium to travel through Mechanical wave

  44. A wave that requires a physical medium to travel through Mechanical wave

  45. A wave that requires a physical medium to travel through Mechanical wave

  46. A wave that requires a physical medium to travel through Mechanical wave

  47. A wave that requires a physical medium to travel through Mechanical wave

  48. A wave that requires a physical medium to travel through Mechanical wave

  49. A wave that requires a physical medium to travel through Mechanical wave

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