The Nature of Waves | Physics in Motion — Transcript

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1. 0:00♪♪
2. 0:20Nothing like listening to the sound of ocean waves
3. 0:22to learn about the nature of waves.
4. 0:25Waves crashing onto the beach are obvious ones,
5. 0:27but we're just scratching the surface
6. 0:29of what waves are all about.
7. 0:31Think about it.
8. 0:33What are all the different waves you know?
9. 0:35Look up.
10. 0:36Light waves from the sun. That's another wave.
11. 0:39Sound waves from music, voices, laughter.
12. 0:42Waves move in a sine curve.
13. 0:44They have a defined harmonic rhythm.
14. 0:46So, the swinging of a pendulum,
15. 0:48the repeated up and down of a yo-yo or jumping rope,
16. 0:51are all examples of wave motion.
17. 0:53Waves even help us understand earthquakes.
18. 0:56More on that later.
19. 0:58To talk about waves, it's good to know certain key words.
20. 1:01Through the power of video, let's freeze a wave.
21. 1:04The crest is a wave's high point.
22. 1:07The trough is its low point.
23. 1:09To write a wavelength, you use the lambda symbol.
24. 1:12This is a lambda.
25. 1:14One wavelength is measured from the crest to crest,
26. 1:17or trough to trough.
27. 1:19On a graph, let's start from the point of origin
28. 1:22and go to where it touches the x-axis the third time.
29. 1:25That's also one wavelength.
30. 1:27Like ocean waves, other waves don't stand still either.
31. 1:31They move.
32. 1:32If you measure how many wavelengths
33. 1:34pass a certain point,
34. 1:36or count the number of crests that pass by per second,
35. 1:39that's its frequency.
36. 1:41A longer wave will have fewer crests,
37. 1:43which means a lower frequency compared to a shorter wave
38. 1:46moving at the same speed.
39. 1:48The period is the time it takes for a complete wave cycle
40. 1:52to happen from one crest to the next.
41. 1:54So, appropriately, period is written T.
42. 1:57One over a wave's frequency equals its period, T.
43. 2:02And one over period equals frequency, f.
44. 2:05They're reciprocal.
45. 2:06So, here are some periods that all of us experience.
46. 2:09What's the period for the Earth to go around the sun?
47. 2:12About 365 days, right?
48. 2:14And what is the period of the Earth's rotation
49. 2:17spinning around its axis one complete time?
50. 2:20About 24 hours.
51. 2:21If you think about all the different waves,
52. 2:23you can already figure out
53. 2:25there are a lot of factors
54. 2:26influencing the period of a wave.
55. 2:28Here's a wave you probably never realized.
56. 2:31Pendulums make waves, too.
57. 2:33If I move this pendulum,
58. 2:35the period of the wave is how long it takes
59. 2:37to go from one side to the other
60. 2:40and back to its original position.
61. 2:42In this case, the period is in seconds.
62. 2:46Now, if I swing it with a little more force,
63. 2:48the pendulum moves faster, over a longer distance.
64. 2:52So the period stays the same.
65. 2:54With a lighter tap, it moves more slowly,
66. 2:58over a shorter distance.
67. 2:59So, again, the period stays the same.
68. 3:03When the pendulum is at rest,
69. 3:04it's at its equilibrium.
70. 3:07The rhythm and motion varies
71. 3:09depending on the length of the pendulum.
72. 3:12Okay, if I shorten the string, what happens to the wave?
73. 3:17The periodic motion changes.
74. 3:19It swings more quickly, so a faster period.
75. 3:22If I add more length, it swings more slowly,
76. 3:26and the period is much longer.
77. 3:28The formula for the pendulum's period
78. 3:30is T, in seconds, equals two times pi
79. 3:35times the square root of the fraction length, L,
80. 3:39in meters, divided by the acceleration of gravity, g,
81. 3:43which is in meters per seconds square.
82. 3:46So, you can see, in this equation,
83. 3:47gravity affects the pendulum as well.
84. 3:49Gravity is always pulling the pendulum
85. 3:51back to its equilibrium.
86. 3:53The force of gravity on the pendulum
87. 3:55depends upon the pendulum's altitude
88. 3:58or its distance from the center of the earth.
89. 4:00For example, on the moon, gravity is much less,
90. 4:04which means the acceleration is slower,
91. 4:06and the period is much longer than it is on Earth.
92. 4:09By the way, if you add weight to the pendulum,
93. 4:11it doesn't change the period of its wave.
94. 4:13Weight is not a factor.
95. 4:15And some waves, like a pendulum,
96. 4:17have a rhythmic or harmonic motion,
97. 4:19which is a repetition of the wave with the same frequency.
98. 4:23So, think of a wave as a vibration,
99. 4:26a disturbance that moves through space,
100. 4:28and a wavelength shows a wave's complete cycle.
101. 4:31Looking at a wave on a graph,
102. 4:33the x-axis is the wave's equilibrium position
103. 4:36where its height is zero.
104. 4:39A cosine wave is the same as a sine wave,
105. 4:42except it's shifted.
106. 4:44The peak begins higher on the y-axis
107. 4:47instead of the midpoint, like a sine wave does.
108. 4:50The amplitude of a wave is measured from the x-axis
109. 4:54to the peak or crest,
110. 4:55or from the x-axis to the trough.
111. 4:58The distance from the resting point
112. 5:00or equilibrium position to the maximum or minimum intensity.
113. 5:04And, again, the period is the length of time
114. 5:07it takes for a wavelength to pass a point
115. 5:09or to complete a cycle.
116. 5:11And frequency is the number of those cycles
117. 5:14that pass a point in a second.
118. 5:17Most waves that we think about are mechanical waves,
119. 5:20which means they need a medium in which to travel.
120. 5:23Now, what's not a mechanical wave?
121. 5:28Electromagnetic waves, which include radio,
122. 5:31visible light, and x-rays.
123. 5:33They don't need a medium.
124. 5:35They can travel in the void of space just fine.
125. 5:38That's why we can see light from stars
126. 5:40and can pick up radio waves from them.
127. 5:42Now, how fast is a wave moving?
128. 5:45The speed of mechanical waves depends on the medium
129. 5:48they're traveling through.
130. 5:50Sound waves travel more than four times faster in water
131. 5:53than in air.
132. 5:55The velocity of a wave is written with the letter v,
133. 5:58and calculated by multiplying the wave's frequency,
134. 6:00small f, times the wavelength.
135. 6:04There are two ways waves can move.
136. 6:05Can you guess?
137. 6:07Longitudinally and transversely.
138. 6:09Longitudinal waves are compression waves.
139. 6:12They move in the same direction
140. 6:14as the force that creates them.
141. 6:17As these waves move,
142. 6:19they stretch and compress matter or particles in their path.
143. 6:23Here's an example.
144. 6:25When all the coils of this slinky
145. 6:27are equidistant from each other,
146. 6:29this slinky is at rest.
147. 6:30That's its equilibrium position.
148. 6:33Now, let's add a little force.
149. 6:35I'll push one end of the slinky.
150. 6:37Watch what happens to the coils
151. 6:39as the wave passes through.
152. 6:42The coils compress,
153. 6:43which means they get closer to each other
154. 6:46compared to when they were at rest, right?
155. 6:48And they get farther apart here.
156. 6:52Now, think of it like this.
157. 6:54Where they're farthest apart,
158. 6:56you can think that they are more rare
159. 6:58than in other parts of the slinky.
160. 7:00That's called rarefaction.
161. 7:02So, as I keep adding the same force...
162. 7:08with the same rhythmic beat,
163. 7:10the compressed coils move down the length of the slinky.
164. 7:14Check it out.
165. 7:16Compression.
166. 7:17We have created a longitudinal wave.
167. 7:20You'll see in other segments
168. 7:21that sound waves move like this, too.
169. 7:24So, what is the amplitude of these slinky longitudinal waves?
170. 7:29The amplitude is the distance
171. 7:31from the equilibrium position coils at rest
172. 7:35to the maximum or minimum intensity.
173. 7:38The second type of wave is a transverse wave,
174. 7:40which we can also show with a slinky.
175. 7:42They look like sine waves.
176. 7:44Okay, with what you know about waves,
177. 7:47let's go underground because with earthquakes,
178. 7:49you get both transverse and longitudinal waves
179. 7:52of varying magnitudes.
180. 7:55And you've seen the devastation they can cause.
181. 7:57These waves can pack a powerful punch.
182. 8:00When plates in the earth shift,
183. 8:02they create seismic waves.
184. 8:05They're what scientists monitor
185. 8:07to locate the epicenter of the earthquake.
186. 8:09Seismic waves come in two varieties, P and S waves.
187. 8:14P waves, where P stands for primary,
188. 8:17are longitudinal and move quickly through the earth.
189. 8:21S waves are secondary waves.
190. 8:23They're transverse waves.
191. 8:25They travel more slowly and can be very destructive.
192. 8:32Springs make waves, too.
193. 8:34Pull on a spring...
194. 8:36and you can see there's a harmonic action from rest
195. 8:39to bouncing down, and up, and down, and up.
196. 8:43Each spring has a different ability to restore itself.
197. 8:47To bounce back to its equilibrium position.
198. 8:50That's called the spring constant.
199. 8:53The force required to pull the spring
200. 8:55away from its rest position is given by the equation
201. 8:59F equals negative k times x,
202. 9:03where F is the force, k is the spring constant,
203. 9:07and x is the displacement from the rest position.
204. 9:11The negative sign is there
205. 9:13because the force opposes the motion of the spring
206. 9:16getting back to its rest position.
207. 9:19The potential energy of the spring at rest is zero,
208. 9:22but the potential energy of a stretched spring
209. 9:25is one half kx squared.
210. 9:29Here's how to figure out the energy in a spring
211. 9:31that oscillates and has a wavelike motion.
212. 9:34You should know the spring constant,
213. 9:36which describes how stiff or strong the spring is.
214. 9:39The higher the spring constant,
215. 9:41the more force it takes to stretch or compress it.
216. 9:44Every spring has a spring constant,
217. 9:47and it's not always the same for every spring.
218. 9:49Springs are different
219. 9:51because they do not apply constant forces.
220. 9:53The more a spring is stretched,
221. 9:55the greater the force pulls back on you.
222. 9:58So, are you getting the gist of all this wave action?
223. 10:01Just look around you,
224. 10:02and you'll see that waves are everywhere.
225. 10:04Just dive right in.
226. 10:10For more practice problems, lab activities,
227. 10:12and note-taking guides,
228. 10:14check out the "Physics in Motion" toolkit.