Waves. Wikipedia. hfps://

Transcription

1 Waves From your book: All waves are named a5er water waves. Think for a moment about how strange water waves are. Wind pushes up a pile of water, and the pile creates a wave. The wave moves and keeps on moving, carrying energy far from the place where the wave was created. Waves at the coast are frequently an indicator of a distant storm. But the water from that distant storm didn t move very far, just the wave. The wind pushed the water, and the water pushed other water, and the energy traveled for thousands of miles, even though the water only moved a few feet. Wikipedia hfps://

2 Jargon The wave speed is just what it sounds like: the speed that a wave moves. The wave speed depends on the dynamics of the wave. Large waves in deep water and short waves in shallow water are different. Sound waves, waves on a string, electromagnekc waves, all travel at different speeds determined by the dynamics of the wave propagakon.

3 Jargon The wavelength is the distance between two equal parts of the wave. In water waves, the wavelength can vary by many orders of magnitude. You see lifle ripples that are only a millimeter across, and giant tsunami waves that hare 10s of km across! It might bother your English teacher, but wavelength is one word. wavelength

4 Jargon The period is the Kme it takes one wave to go by. The frequency is the number of waves per second that go by. The frequency is 1/period. This is something to consider: the wave speed is just the wavelength divided by the period. So, the speed is also equal to the wavelength Kmes the frequency. wavelength

5 Jargon The period is the Kme it takes one wave to go by. The frequency is the number of waves per second that go by. The frequency is 1/period. This is something to consider: the wave speed is just the wavelength divided by the period. So, the speed is also equal to the wavelength Kmes the frequency. The book calls this the equakon for waves: v = fl It s prefy important, but don t memorize. wavelength

6 Wave packets From your book: Waves can be long with many vibrakons, as when you hum, or they can be short, as in a shout. We call such short waves wave packets. You may have nokced that water waves o5en travel in packets. Splash a rock into a pool, and you ll see a bunch of waves moving out, forming a ring that contains several up and down oscillakons. That s a packet. A shout contains many oscillakons of the air, but these oscillakons are confined to a relakvely small region. So that too is a wave packet. hfps:// Now think about this: short waves act in a way very similar to parkcles. They move and they bounce. They carry energy. If the packet were extremely short, maybe you wouldn t nokce that it was really a wave. Maybe you would think that it was a small parkcle.

7 On-line demo hfp://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html

8 hfps:// Two categories of waves Physicists like to separate waves into two categories: called longitudinal and transverse. Transverse waves are those where the vibrakon is perpendicular to the wave mokon. For example, when you shake a rope like in the previous demo, the wave moves down the length of the rope, but the individual segments of the rope move up and down Longitudinal waves are when the shaking is in line with the mokon of the wave. For example, waves in a slinky:

9 Water waves Water waves are both longitudinal and transverse. If you are swimming or floakng and a water wave passes by, you move slightly back and forth as well as up and down: hfps://

10 Speed of water waves The propagakon of water waves depends on interackon of the wave with the bofom. If the wavelength is larger than, or about the same as, the depth, then the wave is said to be shallow. If the wavelength is smaller than the depth, then the wave is said to be deep. In this context, shallow and deep do not have meaning except comparing the wavelength to the depth.

11 Speed of water waves Shallow water wave speed depends only on the depth D: speed (m/s) 3.1 D Deep water wave speed depends only on the wavelength L: speed (m/s) 1.2 L

12 Speed of water waves Shallow water wave speed depends only on the depth D: speed (m/s) 3.1 D Think about this: Tsunami waves are generally very large, and can exceed 10 km in wavelength. That is longer than the depth of the ocean, so tsunami waves are shallow water waves even in the deep ocean. For a depth of 3 km, we get a speed of 170 m/s, which is half the speed of sound. Can you outrun a tsunami wave?

13 Speed of water waves Deep water wave speed depends only on the wavelength L: speed (m/s) 1.2 L In deep water, longer waves travel faster than shorter ones: hfps://

14 Sound waves From your book: Sound is generated in air when something compresses it in a local region. This could be the vibrakng of vocal cords, a violin string, or a bell. The compressed air expands, and compresses the air next to it. The air never moves very far, but the compression is passed on from one region to the next. hfp:// Each molecule shakes back and forth and doesn t travel very far, but the waves travel forward (at the speed of sound).

15 Speed of sound waves The speed of sound depends on how skff the material is. Air is not very skff, and has a relakvely low speed of sound compared to solids. The speed of sound depends on temperature but not pressure*. However the temperature dependence is weak: Material and Temperature Air at 0 C Air at 20 C Water at 0 C Water at 20 C Steel Speed of sound 331 m/s (one mile in 5 seconds) 343 m/s 1402 m/s = 1.4 km/s 1482 m/s = almost 1 mile/second 5790 m/s = 3.6 miles per second The speed of sound (mostly) does not depend on how loud the sound is! *For gasses at high pressure, the speed of sound can increase.

16 Refrac=on: a property of all waves When waves move in a region where the speed changes, the waves can change direckon! Waves tend to change their direckon by bending their mokon toward the side that has a slower wave speed. faster wave speed slower wave speed

17 Sound waves bend hfp://mateeriaharutus.blogspot.com/2011/08/refraktsioon-ja-diffraktsioon.html

18 Sound waves bend Cool air (slower sound) Warm air (faster sound) Warm air (faster sound) Cool air (slower sound)

19 Sound waves bend Cool air (slower sound) No sound reaches here Warm air (faster sound) Sound is channeled further

20 Be careful! Be careful reading the book about this subject: Morning and evening in California (where the author lives) are quite different from Texas. Also, temperature inversions in Texas are very seasonal. For example, I frequently hear the Texas World Speedway on cold Saturday mornings, as depicted in the plot on the previous slide. However, the author discusses this as evening where he lives.

21 Earthquakes When a fault in the Earth suddenly releases energy, it creates a wave that travels through the Earth. We usually hear earthquakes characterized in terms of their magnitude on the Richter scale. GeoscienKsts actually do not like this characterizakon, because the destruckon resulkng from an earthquake depends on very many things. But so far all the scienksts afempt to use alternakve measures have failed. Just as we are stuck with Fahrenheit, we are stuck with the Richter scale. One magnitude on this scale represents a factor of 30 in energy. Two magnitudes represents a factor of 1000 in energy. Magnitude Energy released 6 15 kilotons of TNT kilotons megaton megatons gigatons

22 Seismic waves Earthquakes release both longitudinal and transverse waves that travel at different speeds. Knowing the difference in these speeds allows seismologists to calculate the distance to the epicenter of an earth quake. Having mulkple seismographs allows triangulakon to find the exact point of the quake. The transverse waves cannot travel in liquid, and this has allowed scienksts to build our current model of the earth as a solid iron core, with a liquid outer core, and a solid mantle.

23 Interference If you have two waves, they can add up. Depending on how they add, the result can be a stronger or weaker wave. Wikipedia

24 Wave Interference hfps://

25 Wave Interference

26 Interference - beats

27 Interference - beats

28 Interference hfps://

29 Light is a wave hfps://

30 The Doppler Effect hfps://

31

32 Review 1 The speed of a wave is the wavelength divided by the period, which is equal to the wavelength mulkplied by the frequency. Waves can be divided into two categories: transverse and longitudinal. VibraKons on a string and light are transverse waves. Sound is a longitudinal wave. Water waves are a combinakon of transverse and longitudinal. Water waves with a wavelength longer than the depth of the water have a speed that depends on the square root of the depth. Water waves with a wavelength less than the depth of the water have a speed that depends on the square root of the wavelength. Tsunami waves typically have very long wavelength -- longer than the depth of the ocean, and move at over a hundred meters per second. The speed of sound waves depends on the material and its temperature. Sound takes about 5 seconds to travel one mile in air, and about 1 second to travel a mile in water.

33 Review 2 Waves bend when their speed changes. Waves bend toward a region of lower speed. When the air near the ground is cold and increses temperature with alktude, sound is focussed near the ground and carries further. When the air near the ground is hofer, sound is bent into the air, and a "shadow" can be produced where the sound waves don't reach. Earthquakes release both longitudinal and transverse waves that travel at different speeds. Each magnitude of an earthquake releases 30 Kmes as much energy. Interference is when waves overlap, and can add or subtract in amplitude. Beats are interference of sound waves; the beat frequency is just the difference of the wave frequency. The Doppler effect is the shi5ing of a wave frequency when the source is in mokon relakve to the observer.