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# Waves

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### Waves

1. 1. Waves and Vibrations
2. 2. Objectives <ul><li>describe the difference between a longitudinal wave and a transverse wave </li></ul><ul><li>identify the parts of a wave </li></ul><ul><li>calculate wave speed when frequency and wavelength are given </li></ul>
3. 3. Key Terms
4. 4. Waves are everywhere in nature <ul><ul><li>Sound waves </li></ul></ul><ul><ul><li>light waves </li></ul></ul><ul><ul><li>radio waves </li></ul></ul><ul><ul><li>microwaves </li></ul></ul><ul><ul><li>water waves </li></ul></ul><ul><ul><li>telephone cord waves </li></ul></ul><ul><ul><li>stadium waves </li></ul></ul><ul><ul><li>earthquake waves </li></ul></ul><ul><ul><li>waves on a string </li></ul></ul><ul><ul><li>slinky waves </li></ul></ul>
5. 5. What is a wave? <ul><li>a wave is a disturbance that travels through a medium from one location to another. </li></ul><ul><li>the wave is the motion of a disturbance </li></ul>
6. 6. Slinky Wave <ul><li>Let’s use a slinky wave as an example. </li></ul><ul><li>When the slinky is stretched from end to end and is held at rest, it assumes a natural position known as the equilibrium or rest position </li></ul><ul><li>To create a wave here we must first create a disturbance. </li></ul>
7. 7. Slinky Wave <ul><li>One way to do this is to quickly push the slinky forward </li></ul><ul><li>the disturbance moves down the slinky </li></ul><ul><li>this disturbance that moves down the slinky is called a pulse . </li></ul>
9. 9. Slinky Wave <ul><li>This disturbance would look something like this </li></ul><ul><li>This type of wave is called a LONGITUDINAL wave. </li></ul><ul><li>The pulse is transferred through the medium of the slinky, but the slinky itself does not actually move. </li></ul><ul><li>So what really is being transferred? </li></ul>
10. 10. Slinky Wave <ul><li>Energy is being transferred. </li></ul><ul><li>The metal of the slinky is the MEDIUM in that transfers the energy pulse of the wave. </li></ul><ul><li>The medium ends up in the same place as it started … it just gets disturbed and then returns to it rest position. </li></ul><ul><li>The same can be seen with a stadium wave . </li></ul>
11. 11. Longitudinal Wave <ul><li>In a longitudinal wave, the medium particles vibrate parallel to the motion of the pulse. </li></ul><ul><li>This is the type of wave that transfers sound. </li></ul>
12. 12. Transverse waves <ul><li>A second type of wave is a transverse wave. </li></ul><ul><li>Remember, in a longitudinal wave the pulse travels in a direction parallel to the disturbance. </li></ul><ul><li>In a transverse wave the pulse travels perpendicular to the disturbance. </li></ul>
13. 13. Transverse Waves <ul><li>The differences between the two can be seen </li></ul>
14. 14. Transverse Waves <ul><li>Transverse waves occur when we wiggle the slinky back and forth. </li></ul>
15. 15. Transverse v. Longitudinal
16. 16. Anatomy of a Wave <ul><li>Now we can begin to describe the anatomy of our waves. </li></ul><ul><li>We will use a transverse wave to describe this since it is easier to see the pieces. </li></ul>
17. 17. Anatomy of a Wave <ul><li>In our wave here the blue line is the wave and the solid grey line is the equilibrium position </li></ul><ul><li>Once the medium is disturbed, the medium moves away from equilibrium and then returns to it </li></ul>equilibrium
18. 18. Anatomy of a Wave <ul><li>The points A and B are called the CRESTS of the wave. </li></ul><ul><li>This is the point where the wave exhibits the maximum amount of positive or upwards displacement </li></ul>A B crest
19. 19. Anatomy of a Wave <ul><li>Point C is called the TROUGH of the wave. </li></ul><ul><li>This is the point where the wave exhibits its maximum negative or downward displacement. </li></ul>C trough
20. 20. Anatomy of a Wave <ul><li>The height of the wave – as measured from equilibrium to crest is called the amplitude </li></ul><ul><li>This is the maximum displacement that the wave moves away from its equilibrium. </li></ul>Amplitude A crest
21. 21. Anatomy of a Wave <ul><li>The distance between two consecutive similar points (in this case two crests) is called the wavelength . </li></ul><ul><li>Between what other points is can a wavelength be measured? </li></ul>wavelength
22. 22. Wave frequency <ul><li>We know that frequency measures how often something happens over a certain amount of time. </li></ul><ul><li>A wave’s frequency is measured by how many complete waves pass a fixed point in a certain amount of time </li></ul>
23. 23. Wave frequency <ul><li>Suppose I wiggle a slinky back and forth, and count that 6 waves pass a point in 2 seconds. What would the frequency be? </li></ul><ul><li>3 waves / second </li></ul><ul><li>3 Hertz </li></ul><ul><li>Hertz = Hz. </li></ul>
24. 24. Wave frequency <ul><li>Suppose I wiggle a slinky back and forth, and count that 27 waves pass a point in 1 second. What would the frequency be? </li></ul><ul><li>27 waves / second </li></ul><ul><li>27 Hertz </li></ul>
25. 25. Wave frequency <ul><li>Can you create a formula for frequency? </li></ul><ul><li>frequency = # of waves that pass by / time </li></ul><ul><li>Frequency is measured in Hertz (Hz) </li></ul>
26. 26. Wave Speed <ul><li>Think back to what you know about motion: what is the formula for speed? </li></ul><ul><li>speed = distance / time </li></ul><ul><li>so to calculate speed, we need to know two things: </li></ul><ul><li>1. distance </li></ul><ul><li>2. time </li></ul>
27. 27. Wave Speed <ul><li>Let’s apply what we know about speed to waves: </li></ul><ul><li>A set of waves passes a point 5 times in one second (5 Hz) </li></ul><ul><li>Each wave is 4 cm long </li></ul><ul><li>What is the total distance traveled? </li></ul><ul><li>How long does it take the waves to travel this distance? </li></ul>
28. 28. Wave Speed <ul><li>5 waves that are 4 cm long each = 20 cm </li></ul><ul><li>it takes these five waves one second to pass by </li></ul><ul><li>speed = distance/time </li></ul><ul><li>what’s the wave’s speed? </li></ul><ul><li>Answer = 20 cm/s </li></ul>
29. 29. Wave Speed <ul><li>Here’s another problem: </li></ul><ul><li>10 waves pass by in two seconds (5 Hz) </li></ul><ul><li>each wave is 3 m in length </li></ul>
30. 30. Wave Speed <ul><li>Total distance = 30m </li></ul><ul><li>time = 2s </li></ul><ul><li>Speed? </li></ul><ul><li>Answer: 15m/s </li></ul>
31. 31. Wave Speed <ul><li>The problems I’m giving you can be reasoned out… </li></ul><ul><li>but what if you wanted (or needed) a formula? </li></ul>
32. 32. Wave Speed Formula <ul><li>Let’s look at another problem with easy numbers: </li></ul><ul><li>5 waves pass by in a second; each wave is 2 cm long </li></ul><ul><li>the total distance traveled by all waves is 10 cm, the time it takes them to pass by is 1 second, so the speed is 10 cm/s </li></ul>
33. 33. Wave Speed Formula <ul><li>5 waves pass by in a second (frequency); each wave is 2 cm long (wavelength) </li></ul><ul><li>the speed is 10 cm/s </li></ul><ul><li>what is the relationship between the speed, frequency, and wavelength in the problem? </li></ul>
34. 34. Wave Speed Formula <ul><li>If given frequency (Hz or waves/s), and wavelength, the formula for wave speed is: </li></ul><ul><li>frequency x wavelength = wave speed </li></ul>
35. 35. Exit Slip <ul><li>Describe the differences between a longitudinal and transverse wave. </li></ul><ul><li>Draw a transverse wave and label the wavelength, amplitude, crest, and trough. </li></ul><ul><li>If the wavelength is 20 cm and frequency is 5Hz, what is the wave’s speed? SHOW YOUR WORK! </li></ul>