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Waves

Waves. April 19, 2010. What do you know?. Name all the different types of waves you can think of… What does a wave do? Or why does nature need waves? Consider the result if there were no waves Think of the Dec 26, 2004 Tsunami…. Hooke’s Law. The force of a spring changes

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Waves

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  1. Waves April 19, 2010

  2. What do you know? • Name all the different types of waves you can think of… • What does a wave do? • Or why does nature need waves? • Consider the result if there were no waves • Think of the Dec 26, 2004 Tsunami…

  3. Hooke’s Law • The force of a spring changes • Depending on how far you stretch it • Turns out …F = -ks • If a mass is hanging off a spring • ΣF = ma • At rest… Fs – W = ma = 0

  4. Boing… • A mass of 2.4 kg is suspended from a spring. • The weight stretches the spring 0.13 m. • Determine the spring constant for the spring.

  5. Waves start with periodic motion… • AKA Simple Harmonic Motion • SHM • For example… • Springs • Pendulum

  6. Periodic Motion • What makes it so? • Back and forth along the same path. • Position, speed and acceleration • All repeat on same cycle • Spring • When is it at max speed? • When is it at max acceleration? • Pendulum?

  7. Describing Periodic Motion • Frequency (f) • Number of cycles per unit time • 1/seconds = Hz • Period (T) • Time to go through a complete cycle • Seconds • T = 1/f • A pendulum goes through 5 cycles in 10 seconds. • What is its period? • Its frequency?

  8. Pendulums’ Period - Galileo figured it out • Mass has nothing to do with it • Just like free fall!! • The amplitude doesn’t affect it either! • It does depend on L • T = 2π(L/g)½ • What is the period for a pendulum with a length of 1.8 meters?

  9. Quick Recap • What is frequency? • What is period? • How long of string would give you a period of 1 second? • T = 2π(L/g)½ • L = 0.25 meters

  10. The nature of waves • Imagine a buoy on the ocean… • What happens to it as waves go by?

  11. Why waves? • The “stuff” stays put • Waves carry energy from place to place

  12. Wave Properties • Crest = Top of Wave • Trough = Bottom of Wave • Wavelength = length for one cycle • Amplitude versus wave height?

  13. Speed • Measured in meters per second. • v = wave length x frequency • Or… • V = λ f • Speed is constant for a given medium…

  14. For a spring • Period is related to a couple things… • Any ideas?

  15. Spring Lab • Does the period of a spring depend on • The distance stretched? • The k value? • 3 springs • Find “k” • Measure Δs • Then 3 trials each • Different stretches • Use the same mass

  16. Waves April 21, 2010

  17. 441 3) 2700 N/m 4) 81 N 449 140 m 0.25 m 3.6 m 451 210 N/m 25 N/m Homework

  18. Lab: T of springs • What affected the period? • T = 2π(m/k)½ • How close does your data fit?

  19. Waves • Two types of waves • Mechanical • Electromagnetic • Mechanical • Require a medium • Like air, or water, or string, or spring • Electromagnetic • They are special – no medium required

  20. Mechanical Waves • Two types of mechanical waves • Transverse • Longitudinal • What is the difference? • Transverse wiggles perpendicular (across)… • Longitudinal wiggles along the wave direction

  21. Transverse Waves • Classic sinusoidal wave • Crest • Trough • Wavelength • Amplitude

  22. Longitudinal Waves • Pressure wave • Sections of • compression • rarefaction (stretch) • Sound is a longitudinal wave

  23. Wave Speed • Velocity = wavelength x frequency • V = λf • (Distance of 1 cycle) / (time for 1 cycle) • Speed of a mechanical wave is constant for any given medium • Wise up other my mixed words would be.

  24. Example • Piano – middle C has a frequency of 264 Hz • The velocity of sound in air is 343 m/s • What is the wavelength of the middle C? • V = λf • λ = v/f • 343 m/s / 264 Hz = 1.30 meters

  25. Does it repeat? • If it does… • It is a periodic wave • If not… • It is a pulse

  26. Interference • What happens when waves overlap or touch

  27. Interference • Can be Constructive • crest lines up with another resulting in adding effect • More or less energy?

  28. Interference • Or can be Destructive • Crest overlaps a trough resulting in reducing effect. • Smaller amplitude

  29. USCGC Ironwood

  30. Reflection • If you send a pulse through a medium and it strikes a barrier • What do you think happens to the wave? • It depends…

  31. Standing waves • They are the result of interference • Nodes and antinodes…

  32. Slinky Lab • Read the lab carefully! • Several exercises with slinkies • Pulses • Periodic waves • Standing waves • Nodes • Spread out around the room

  33. Mechanical Waves April 23, 2010

  34. In the southern seas… • Heading into the ice…

  35. Today • Notes on Waves • Sound • Doppler • Lab – A day at the beach

  36. Sound waves • Sound waves are compression waves • Longitudinal waves • Move out in a 3-D sphere • We hear certain frequencies • 20 – 20,000 Hz • Different animals…different frequencies • Dogs, elephants, frogs

  37. Sound wave properties • Amplitude – • How loud the sound is • Related to its energy • Frequency and wavelength • The pitch (how high or low the note is) • Generally speaking… • Speed is greater through solids than liquids • And liquids faster than in air

  38. Doppler Effect • Sound from a stationary object goes out in all directions • A spherical wave • Produces a ripple

  39. Doppler • What happens when you move the object? • It gets closer to the wave that just left… • The space between the waves decreases • Wavelength gets smaller

  40. Doppler: v = λf still applies • If the wavelength gets smaller • The frequency must get bigger • Remember: • Velocity = wavelength x frequency

  41. Hmmm… • If you ran towards a car… • Would you get the same effect?

  42. Break the sound barrier

  43. Lab – at the beach! • Explores the relationship between depth of water and the speed of waves • What do you think???? • Consider what we’ve learned about Interference & Doppler (not part of lab)

  44. Sound Waves April 27, 2010

  45. Plan changes • Survey monkey says… • Lab makeup time today • Lesson will stretch over

  46. Key points • Intensity • Forced Vibrations and Resonance • Beats

  47. Sound intensity • Tied to amplitude of the waves • Intensity • The amount of power per unit area • I = P/A (Watts per meter2) • For a spherical wave (like sound): • I = P/4πr2 • This is the wave intensity of sound at some distance “r” from the source!

  48. Intensity • Note the relationship: • I = P/4πr2 • As distance increases… • The intensity changes by the inverse square • Units are Watts/m2

  49. Our ears are logarithmic… • If you double the intensity of a sound • We perceive a slight increase in loudness • In order to double the loudness the intensity must increase 10 times! • We developed a scale that lets us manage this easier • The decibel scale

  50. Decibels (dB) • The relative intensity • Relates the intensity to our hearing threshold • 0 dB – can’t hear it • 50 dB – normal conversation • 70 dB – vacuum cleaner • 90 dB – lawn mower • 120 dB – pain threshold • Note that this is NOT the frequency… • But is the LOUDNESS!

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