Lecture 13
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Waves can be characterized by their wavelength, amplitude, frequency, and period. The wavelength is the distance between matching portions of two waves, amplitude is the height of the wave, frequency is the number of waves per second, and period is the time for one full cycle. The relationship between frequency and period is that frequency equals 1 divided by period, and period equals 1 divided by frequency. When a wave passes through a medium, the medium itself does not move but rather gets displaced in an up and down or side to side motion depending on if it is a longitudinal or transverse wave.
Lecture 13
- 1. Waves
- 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 cycle Naming stuff for waves:
- 3. Relationship between frequency and period • Frequency = 1/period • Period = 1/frequency Example Problem: Gusts of wind cause the Sears Building in Chicago to sway back and forth completing a cycle every 10 seconds. a) What is the period? b) What is the frequency?
- 4. Example problem • Identify the following: – period – amplitude • Calculate: – frequency -4 -3 -2 -1 0 1 2 3 4 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Displacement(m) Time (s)
- 5. Wave motion • When a wave passes, the medium itself does not move. – It just gets displaced. – The blue dot follows the red circle. Overall it goes nowhere. – The speed of sound is 340 m/s. Clearly the air does not move this fast (what wind).
- 6. Wave speed • The speed of a wave’s motion is related to its frequency and wavelength: – velocity = frequency * wavelength If the wavelength is 1 m and one wavelength per second passes the pole, then the speed of the wave is 1 m/s.
- 7. Example Problem • The speed of sound is 340 m/s. – What is the wavelength of a sound with a frequency of 220 Hz? – What is the frequency of a sound with a wavelength of 10 cm?
- 8. Transverse and Longitudinal Waves • Longitudinal waves: waves which move by compression/rarification. – Prime example: sound • Transverse waves: waves which move by lateral vibration. – Prime example: ocean waves • Demo!
- 9. • Recall our description of a gas. – gas particles may be locally more or less dense, it is easy to move them and compress them. • Wavelength of a sound wave is the distance between successive compressions/rarefactions. • Human ear can typically hear from about 20 Hz to 20,000 Hz. – Shrinks as we age. – Mosquito ring tone Sound Waves
- 10. Sound 2 • Any material that can vibrate can transmit sound. – air – liquid (sound travels better in water: sonar) – solid • Speakers work by vibrating a cone (using an electromagnet and a permanent magnet) which causes nearby air to vibrate. • (rubens tube)
- 11. Example Problems • How does a tuning fork emit sound? • Why does sound travel faster in warm air?
- 12. Forced Vibration and Natural Frequencies • A vibrating object in contact with another object will tend to force vibrations in the other object. • Every elastic object (everything) has its own set of natural frequencies at which it will vibrate. – depends on shape, elasticity, etc. – Sound of an object when it is struck or falls is produced, in part, by these frequencies.
- 13. Resonance • Good example: pumping your legs on a swing to increase the amplitude. – The frequency you swing your legs matches the resonance frequency of the swing. • Another example: one tuning fork driving another.
- 14. Resonance 2 • Resonance may be destructive. – Shattering a wine glass with sound by driving it at a natural frequency. – Bridge collapse (video) • Example Problem: – When you listen to a radio, why do you hear only one station at a time instead of all stations at once?
- 15. Interference • Waves may interact with one another. – At any point their amplitudes may sum. • If two waves happen to meet when their amplitudes are peaked you get reinforcement. • If one wave at its trough of one meets another at its peak you get cancellation.
- 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. Demo • Detuned tuning fork and normal tuning fork form beats.
- 18. Standing Waves • When a wave reflects back on itself you get standing waves. • String vibrates up and down in place. • Places which do not move are called nodes. • Places of maximum motion are antinodes.
- 19. Demo: Standing Waves • There are resonance frequencies available to any standing wave. • fundamental and following tones.
- 20. Example Problem • Distinguish between constructive and destructive interference. • Suppose a piano tuner hears three beats per second when listening to the combined sound from his tuning fork and the piano note being tuned. After slightly tightening the string he hears five beats per second. Should the string be tightened or loosened?