Intro to Waves

1. Intro to Waves

2. What is a wave? • Take a moment to answer this question with the students at your table. • As a group, create a definitionand give an exampleof a wave. (Be a bit more original than ‘an ocean wave.’ I know you can think of a better example…)

3. a wave is a rhythmic disturbance that carries energy through matter or space

4. Mechanical Waves • require a medium • medium: the matter through which a wave travels • examples: water, air, anything made of matter

5. waves transfer energy from one point to another with little or no permanent displacement to the particles in the medium

6. Two Types of Mechanical Waves: • Transverse Waves • Longitudinal Waves

7. Transverse Waves • waves that propagate (or move) perpendicular to the direction of travel

8. crest • the point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position

9. trough • the point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position

10. amplitude • the maximum displacement of a particle on the medium from its equilibrium position

11. wavelength • the length of one wave is measured from a point on one wave to the same point on the next wave • trough to trough • crest to crest • midpoint to midpoint

12. Anatomy of a Transverse Wave • Label the following parts of a transverse wave in your notes: • equilibrium • crest • trough • amplitude • wavelength

13. Longitudinal Waves • waves that propagate (or move) parallel to the direction of motion

14. compression • a point on a medium through which a longitudinal wave is traveling that has the maximum density

15. rarefaction • a point on a medium through which a longitudinal wave is traveling that has the minimum density

16. Anatomy of a Longitudinal Wave • Label the following parts of a longitudinal wave in your notes: • compression • rarefaction • wavelength

17. Describing a Wave • frequency: the number of vibrations an object makes in a unit of time (generally one second) • the unit of frequency is Hz • period: the time needed to complete one vibration (measured in seconds)

18. The Sears Tower sways back and forth at a frequency of about .1 Hz. What is the period of vibration?

19. Speed Review • an object’s speed is described by the distance traveled in a specific amount of time (generally measured in m/s)

20. Wave Speed v = λ●f wave speed = wavelength ● frequency

21. A wave with a frequency of 60.0 Hz travels through vulcanized rubber with a wavelength of 0.90 m. What is the speed of this wave?

22. The lowest pitch that the average human can hear has a frequency of 20.0 Hz. If sound with this frequency travels through air with a speed of 343 m/s, what is its wavelength?

23. A ship anchored at sea is rocked by waves that have crests 14 m apart. The waves travel at 7.0 m/s. How often do the wave crests reach the ship?

24. Earthquakes generate shock waves that travel through Earth’s interior to other parts of the world. The fastest of these waves are longitudinal waves, like sound waves, and are called primary waves, or just p-waves. A p-wave has a very low frequency, typically around 0.050 Hz. If the speed of a p-wave with this frequency is 8.0 km/s, what is its wavelength?

25. A dolphin can typically hear sounds with frequencies up to 150 kHz. What is the speed of sound in water if a wave with this frequency has a wavelength of .01 m?

26. Sonar is a device that uses reflected sound waves to measure underwater depths. There is a sonar signal that has a frequency of 288 Hz. If the speed of sound in water is 1.45x103 m/s, what is the wavelength of the sonar signal?

27. Cicadas produce a buzzing sound that has a wavelength in air of 2.69 m. If the speed of sound in air is 343 m/s, what is the frequency of the sound produced by a cicada? What is its period?

28. A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4 s later. What is the speed of sound of the hiker’s voice in air? The wavelength of the sound is .75 m. What is its frequency? What is the period of the wave?

29. Wave Behavior • What happens when a ball is thrown against a wall? • Predict what would happen if a wave encounters a rigid boundary?

30. When a wave pulse is sent down a medium connected to a rigid wall, the energy transmitted is reflected. • The reflected wave is inverted due to Newton’s Third Law of Motion.

31. Predict what would happen if two waves were in the same place on a medium. • Principle of Superposition • the displacement of a medium caused by two or more waves is the algebraic sum of the displacements of the individual waves • two or more waves can combine to form a new wave • the result of the superposition of two or more waves is called interference

32. Two Types of Interference • Constructive • Destructive

33. Constructive Interference • occurs when wave displacements are in the same direction • the two waves pass through each other without changing their shapes or sizes • the resultant pulse at the overlap of the two waves is the algebraic sum

34. Constructive Interference

35. Destructive Interference • the superposition of waves with equal but opposite amplitudes • when the pulses meet at the same location, the displacement of the medium is zero • just as constructive interference, the waves pass through one another unchanged

36. Destructive Interference

37. Standing Waves • a wave pattern that remains in a constant position • the result of reflection and wave interference • characterized by two fixed points on the wave

39. Tacoma Narrows Bridge • In an effort to save money, corners were cut in the design of the bridge thus compromising its stability • On November 7, 1940 the Tacoma Narrows suspension bridge collapsed due to 42 mph wind induced vibrations.