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# Lecture 13

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### Lecture 13

1. 1. Waves
2. 2. • Wavelength– The distance between matching portions of two waves.• Amplitude– The height above the midpoint of the wave.• Frequency– The number of waves occurring each second.• Period– The time required to complete one cycleNaming stuff for waves:
3. 3. Relationship between frequency andperiod• Frequency = 1/period• Period = 1/frequencyExample Problem:Gusts of wind cause the Sears Building in Chicago tosway back and forth completing a cycle every 10seconds.a) What is the period?b) What is the frequency?
4. 4. Example problem• Identify the following:– period– amplitude• Calculate:– frequency-4-3-2-1012340 0.25 0.5 0.75 1 1.25 1.5 1.75 2Displacement(m)Time (s)
5. 5. Wave motion• When a wave passes,the medium itself doesnot move.– It just gets displaced.– The blue dot follows thered circle. Overall it goesnowhere.– The speed of sound is340 m/s. Clearly the airdoes not move this fast(what wind).
6. 6. Wave speed• The speed of a wave’s motion is related to itsfrequency and wavelength:– velocity = frequency * wavelengthIf the wavelengthis 1 m and onewavelength persecond passesthe pole, thenthe speed of thewave is 1 m/s.
7. 7. Example Problem• The speed of sound is 340 m/s.– What is the wavelength of a sound with a frequencyof 220 Hz?– What is the frequency of a sound with a wavelengthof 10 cm?
8. 8. Transverse and Longitudinal Waves• Longitudinal waves: waves which move bycompression/rarification.– Prime example: sound• Transverse waves: waves which move by lateral vibration.– Prime example: ocean waves• Demo!
9. 9. • Recall our description of a gas.– gas particles may be locally more or less dense, it is easy to move them and compressthem.• Wavelength of a sound wave is the distance between successivecompressions/rarefactions.• Human ear can typically hear from about 20 Hz to 20,000 Hz.– Shrinks as we age.– Mosquito ring toneSound Waves
10. 10. Sound 2• Any material that can vibrate can transmitsound.– air– liquid (sound travels better in water: sonar)– solid• Speakers work by vibrating a cone (using anelectromagnet and a permanent magnet) whichcauses nearby air to vibrate.• (rubens tube)
11. 11. Example Problems• How does a tuning fork emit sound?• Why does sound travel faster in warm air?
12. 12. Forced Vibration and NaturalFrequencies• A vibrating object in contact with another objectwill tend to force vibrations in the other object.• Every elastic object (everything) has its ownset of natural frequencies at which it willvibrate.– depends on shape, elasticity, etc.– Sound of an object when it is struck or falls isproduced, in part, by these frequencies.
13. 13. Resonance• Good example: pumping your legs on a swing to increase theamplitude.– The frequency you swing your legs matches the resonance frequency ofthe swing.• Another example: one tuning fork driving another.
14. 14. Resonance 2• Resonance may be destructive.– Shattering a wine glass with sound by driving it at anatural frequency.– Bridge collapse (video)• Example Problem:– When you listen to a radio, why do you hear onlyone station at a time instead of all stations at once?
15. 15. Interference• Waves may interact with one another.– At any point their amplitudes may sum.• If two waves happen to meet when their amplitudesare peaked you get reinforcement.• If one wave at its trough of one meets another at itspeak you get cancellation.
16. 16. Beats• Beats may be familiar to anyone who has tuned a guitar.– Waves at two frequencies meet.• Sometimes they meet constructively.• Sometimes destructively.• The result is we hear the amplitude of the sound increasing and decreasing.
17. 17. Demo• Detuned tuning fork and normal tuning forkform beats.
18. 18. Standing Waves• When a wave reflectsback on itself you getstanding waves.• String vibrates up anddown in place.• Places which do notmove are called nodes.• Places of maximummotion are antinodes.
19. 19. Demo: Standing Waves• There are resonancefrequencies available toany standing wave.• fundamental andfollowing tones.
20. 20. Example Problem• Distinguish between constructive and destructiveinterference.• Suppose a piano tuner hears three beats per secondwhen listening to the combined sound from his tuningfork and the piano note being tuned. After slightlytightening the string he hears five beats per second.Should the string be tightened or loosened?