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Standing Waves

Standing Waves. A standing wave is the result of two waves of the same frequency and amplitude traveling in the opposite directions through the same medium. Standing Waves. A point of no disturbance in a standing wave is called a node .

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Standing Waves

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  1. Standing Waves • A standing wave is the result of two waves of the same frequency and amplitude traveling in the opposite directions through the same medium.

  2. Standing Waves • A point of no disturbance in a standing wave is called a node. • A point in standing wave where the amplitude is maximum is called an antinode.

  3. Standing Waves • The fundamental frequency (or natural frequency) of a medium occurs when it vibrates with the simplest standing wave – 2 nodes + 1 antinode.

  4. Standing Waves • The harmonic of a wave is a component frequency of the wave that is an integer multiple of the fundamental frequency. • 1st Harmonic = 5 • 2nd Harmonic = 10 • 3rd Harmonic = 15 • 4th Harmonic = 20

  5. Harmonic Series

  6. Sound Waves Physics 1

  7. Sound • Mechanical waves • Longitudinal • sound • Speed dependent upon two things: • elasticity • density

  8. Sound as a Pressure Wave • Sound is created as a pressure wave. • The air compresses in an area of high pressure (compressions) followed by areas of low pressure where the air expands (rarefactions)

  9. Elasticity & Sound Speed • How much a material will compress under pressure • Material wants to maintain its shape (e.g. steel) • rigid material • LOW elasticity • HIGH speed of sound (FAST) • Material easily deforms (e.g. rubber) • flexible material • HIGH elasticity • LOW speed of sound (SLOW)

  10. Density & Sound Speed • Dependent on material type • Fastest in solids • Then liquids • Then gasses • Density has biggest impact on speed • Within a single medium (e.g. air) temperature can impact speed

  11. Speed of Sound

  12. Speed of Sound For the speed of sound in air, where tc is in degrees Celsius Higher temperature – faster speed of sound

  13. Intensity of Sound The sound intensity is the sound power that passes perpendicular through a surface per unit of surface area.

  14. Intensity of Sound If a source emits sound uniformly in all directions, one can imagine the energy spreading out in a spherical pattern.

  15. Intensity of Sound The smallest sound intensity audible to the human hearing is 1 x 10-12 W/m2. This intensity is called the threshold of hearing (I0). Since human hearing has a wide range, the intensity of audible sounds is compared to the intensity at the threshold of hearing.

  16. Intensity of Sound The sound intensity of a vacuum cleaner is around 1 x 10-5 W/m2. Comparing this intensity to the threshold of hearing,

  17. Intensity of Sound Due to the large comparison, it is more appropriate to express this relative intensity (b) in a logarithmic scale.

  18. Intensity of Sound

  19. Intensity of Sound

  20. Frequency of Sound The perceived frequency of an observer or pitch (fo) of an emitted frequency of a sound source (fs) depends on whether the observer or the source are in motion. The ACTUAL emitted frequency does NOT change!!! http://www.acs.psu.edu/drussell/Demos/doppler/doppler.html http://library.thinkquest.org/27948/doppler.html

  21. Frequency of Sound Source and Observer at rest

  22. Frequency of Sound • fo=frequency perceived by observer • fs=frequency emitted by source • vo=velocity of observer • vs=velocity of source • v=velocity of sound

  23. Frequency of Sound • vs =velocity of source • - (negative) when moving TOWARD observer • + (positive)when moving AWAY from observer • vo =velocity of observer • - (negative)when moving AWAYfrom source • + (positive) when TOWARDsource • v=velocity of sound

  24. Doppler Effect – Moving Source Moving Source

  25. Doppler Effect – Moving Source TOWARDS observer • Wavelength gets smaller as source moves closer to observer • Frequency gets faster/higher/bigger • pitch gets higher

  26. Doppler Effect – Moving SourceAWAY FROM observer • Wavelength gets longer/smaller as source moves away from observer • Frequency gets smaller/lower • pitch gets lower

  27. Frequency of Sound • vs =velocity of source • - (negative) when moving TOWARD observer • + (positive)when moving AWAY from observer • vo =velocity of observer • - (negative)when moving AWAYfrom source • + (positive) when TOWARDsource • v=velocity of sound

  28. Doppler Effect – Moving Observer Moving Observer

  29. Doppler Effect – Moving ObserverTOWARDS source • Wavelength gets smaller as observer moves closer to source • Frequency gets faster/higher/bigger • pitch gets higher

  30. Doppler Effect – Moving ObserverAWAY FROM source • Wavelength gets longer (bigger) as observer moves away from to source • Frequency gets slower/lower/smaller • pitch gets lower

  31. Sonic Booms http://www.acs.psu.edu/drussell/Demos/doppler/doppler.html http://www.falstad.com/ripple/

  32. Breaking sound barrier • http://video.today.msnbc.msn.com/today/49414119#49414119 • http://www.wimp.com/breaksbarrier/

  33. Beats • Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another. • Beat Frequency … • Beat frequency is absolute value of difference between two close frequencies

  34. Resonance • The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object. • The tendency of one object to force another adjoining or interconnected object into vibrational motion is referred to as a forced vibration.

  35. Resonance • Resonance occurs when two interconnected objects share the same vibrational frequency. When one of the objects is vibrating, it forces the second object into vibrational motion. The result is a large vibration.

  36. Resonance • Tacoma Narrows Bridge http://www.youtube.com/watch?v=3mclp9QmCGs

  37. Physics in Music • http://www.youtube.com/watch?v=mh5rh3cbvQA

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