Understanding Waves: Types, Propagation, and Energy Transmission

1. Topic List W a v e s Types of Waves Longitudinal Waves Transverse Waves Surface Waves Frequency Wavelength Period Amplitude Wave speed Transmission of Waves Reflection Refraction Superposition Principle Interference Diffraction Standing Waves & Resonance

2. Waves & Information Marvin the Martian would like to send a message from Mars to Earth. There are two ways of sending a message. He could enclose the message in a rocket and physically send it to Earth. Or, he could send some type of signal, maybe in the form of radio waves. Information can be sent via matter or waves. If sent via waves, nothing material is actually transmitted from sender to receiver. If you talk to a friend, be it in person or on the phone, you are transmitting information via waves. Nothing is physically transported from you to your friend. This would not be the case, however, if you sent him a letter.

3. Waves & Energy Suppose Charlie Brown wants to wake up Snoopy. Some energy is required to rouse Snoopy from his slumber. Like information, energy can also be transmitted via physical objects or waves. Charlie Brown can transmit energy from himself to Snoopy via Woodstock: Woodstock flies over; his kinetic energy is physically transported in the form a little, yellow bird. Alternatively, Charlie Brown could send a pulse down a rope that’s attached to Snoopy’s dog house. The rope itself is not transported, but the pulse and its energy are! pulse

4. Types of Waves • mechanical wave is just a disturbance that propagate through a medium. • Exp. sound; water waves; a pulse traveling on a spring; earthquakes; a “people wave” in a football stadium. • A medium is any material through which a wave travels. • Exp. could be air, water, a spring, the Earth, or even people.

5. Mechanical Waves: Three Types Mechanical waves require a physical medium. The particles in the medium can move in two different ways: either perpendicual or parallel to direction of the wave itself. In a longitudinal wave, the particles in the medium move parallel to the direction of the wave. In a transverse wave, the particles in the medium move perpen-dicular to the direction of the wave. A surface wave is often a combination of the two. Particles typically move in circular or elliptical paths at the surface of a medium. Longitudinal  Parallel Transverse  Perpendicular Surface Combo

6. Longitudinal Waves A whole bunch of kids are waiting in line to get their picture taken with Godzilla. The bully in back pushes the kid in front of him, who bumps into the next kid, and so on down the line. A longitudinal pulse is sent through the line of kids. It’s longitudinal because as each kid gets bumped, he moves forwards, then backwards (red arrow), parallel to the direction of the pulse. The location of the pulse is the point where two kids are being compressed together. The next slide shows how the pulse progresses through the line. pulse direction

7. Ouch! Longitinal Waves (cont.) C = Compression (high kid density) R = Rarefaction (low kid density) The compression (the pulse) moves up the line, but each kid keeps his place in line. C Ouch! R C Ouch! I hope Godzilla eats that bully! C R

8. Sound is a Longitudinal Wave As sound travels through air, water, a solid, etc., the molecules of the medium move back and forth in the direction of the wave, just like the kids in the last example, except the molecules continually move back and forth for as long as the sound persists. If the bully kept shoving the kid in front of him, a series of pulses would be generated. If he shoved with equal force each time and did this at a regular rate, we would call these pulses a wave. Similarly, when a speaker or a tuning fork vibrates, it repeatedly shoves the air in front of it, and a longitudinal wave propagates through to the air. The speaker shoves air molecules; the bully shoves people. In either case, the components of the medium must bump into their neighbors.

9. Transverse Waves After a great performance at a drum and bugle corps contest, the audience decides to start a wave in the stands. Each person rises and sits at just the right time so the effect is similar to the pulse in Charlie Brown’s rope. Like the Godzilla example, people make up the wave medium here. But this is a transverse wave because, as the wave moves across the stands, folks are moving up and down. wave direction

10. Transverse Waves (cont.) In a transverse wave, molecules aren’t being compressed and spread out as they are in a longitudinal wave. The reason a transverse wave can propagate is because of the attraction between adjacent molecules. Imagine if each person in the stands on the last slide were connected to the person on his left and right with giant rubber bands. As soon the person on one end stood up, the band stretches. The tension in the band pulls his neighbor up, who, in turn, lifts the next guy. The tension in the rubber bands is analogous to the forces connecting particles of the medium to their neighbors. The colored sections of rope tug on each other as the waves travels through them. If they didn’t, it would be as if the rope were cut, and no wave could travel through it.

11. Surface Waves Below the surface fluids can typically only transmit longitudinal waves, since the attraction between neighboring molecules is not as strong as in a fluid. At the surface of a lake, water molecules (white dots) move in circular paths, which are partly longitudinal and partly transverse. The molecules are offset, though: when one is at the top of the circle, the one in front of it is near the top. As in any wave, the particles of the medium do not move along with the wave. The water molecules complete a circle each time a crest passes by. wave direction

12. Breaking Waves Waves break near the shore because the water becomes shallow. Close to the shore the ground beneath the water interferes with the circular motions of the water molecules as they participate in a passing wave. Sandbars further off shore can have the same effect, much to the delight of surfing enthusiasts like Bart.

13. Seismic Waves Seismic waves use Earth itself as their medium. Seismic waves can be longitudinal, transverse, or surface waves. P and S type waves are called body waves, since they are not confined to the surface. Rayleigh waves do most of the shaking during a quake.

14. “Mini Seismic” Waves Though we might not refer to them as seismic, anything moving on the ground can transmit waves through the ground. If you stand near a moving locomotive or a heard of charging elephants, you would feel these vibrations. Even something as small as a beetle generates pulses when it moves. These pulses can be detected by a nocturnal sand scorpion. Sensors on its eight legs can detect both longitudinal and surface waves. The scorpion can determine the direction of the waves based on which legs feel the waves first. It can determine the distance of the prey based on the time delay between the fast moving longitudinal waves and the slower moving surface waves. The greater the time delay, the farther away the beetle. This is the same way seismologists determine the distance of a quake’s epicenter. Sand is not the best conductor of waves, so the scorpion will only be able to detect beetles within about a half meter.

15. Wave Characteristics Amplitude (A) – Maximum displacement of particle of the medium from its equilibrium point. The bigger the amplitude, the more energy the wave carries. Wavelength ()– Distance from crest (max positive displacement) to crest; same as distance from trough (max negative displacement) to trough. Period (T) – Time it takes consecutive crests (or troughs) to pass a given point, i.e., the time required for one full cycle of the wave to pass by. Period is the reciprocal of frequency: T = 1/f. Frequency (f) – The number of cycles passing by in a given time. The SI unit for frequency is the Hertz (Hz), which is one cycle per second. Wave speed (v) – How fast the wave is moving (the disturbance itself, not how fast the individual particles are moving, which constantly varies). Speed depends on the medium. We’ll prove that v = f.

16. Amplitude & Wavelength The red transverse wave has the same wavelength as the longitudinal wave in the spring. (P to Q is one full cycle.) Note that where the spring is most compressed, the red wave is at a crest, and where the spring is most stretched (rarified), the red wave is at a trough. The amplitude in the red wave is easy to see. In the longitudinal wave, the amplitude refers to how far a particle on the spring moves to the left or right of its equilibrium point. Often a graph like the red wave is used to represent a longitudinal wave. For sound, the y-axis might be pressure deviation from normal air pressure, and the x-axis might be time or position. P Q A 

17. Frequency & Period Riddle me this…Why is the frequency of a wave the reciprocal of its period? Answer: Period = seconds per cycle. Frequency = cycles per second. They’re reciprocals no matter what unit we use for time. A sound wave that has a frequency of 1,000 Hz has a period of 1/1,000 of a second. This means that 1,000 high pressure fronts are moving through the air and hitting your eardrum each second.

18. Speed, Wavelength, & Frequency Barney Rubble, a.k.a. “Barney the Wave Watcher,” is excited because he just made a discovery: v = f. With some high tech, prehistoric equipment, Barney measures the wavelength of the incoming waves to be 18 ft. He counts 10 crests hitting the shoreline every minute. So, 10 crests pass any given point in a time of one minute. But 10 crests corresponds to a distance of 180 ft, which means the wave is traveling at 180 ft/min. This result is the product of wavelength and frequency, yielding the result: 18 ft v = f

19. Reflection of Waves Whenever a wave encounters different medium, some of the wave may be reflected back, and some of the wave penetrate and be absorbed or transmitted through the new medium. Light waves reflects off of objects. If it didn’t, we would only be able to see objects that emitted their own light. We see the moon because it’s reflecting sunlight. Sound waves also reflect off of objects, creating echoes. Water waves, seismic waves, and waves traveling on a rope all can reflect.

20. Transmission & Reflection • Let’s look at 4 different scenarios of a waves traveling along a rope. • Hard boundary (fixed end): Reflected wave is inverted. • Soft boundary (free end): Reflected wave is upright. • Light rope to heavy rope: Reflected wave is faster and wider than transmitted wave. Transmitted wave is upright, but reflected wave is inverted (since to the thin rope, the thick rope is like a hard boundary). • Heavy rope to light rope: Transmitted wave is faster, wider, and has a greater amplitude than reflected wave. Both waves are upright. (The transmitted wave is upright this time since, to the thick rope, the thin rope is like a soft boundary). • https://www.youtube.com/watch?v=dNmlNzrMF2k

21. Frequency of Transmitted Waves The frequency of a transmitted wave is always unchanged. Say a wave with a frequency of 5 Hz is traveling along a rope that changes thickness at some point. Since 5 pulses hit this point every second, 5 pulses will be transmitted every second. Since the speed will vary depending on the thickness of the rope, the wavelength must vary too. Here a wave travels from a thin rope to a thick one. Because µ is larger in the thick rope, the wave is slower there. This causes the waves to “bunch up,”which means a decrease in wavelength. (For clarity the reflected waves are not shown here.) v v

22. Amplitude of Reflected & Transmitted Waves: Light to Heavy When a pulse on the light rope reaches the interface, the heavy rope offers a lot of resistance. The heavy rope is not affected much by the light rope, so the transmitted pulse has a smaller amplitude. The reflected pulse’s amplitude diminishes since some of the light rope’s energy it transmitted to the heavy rope. before incident pulse inverted reflected pulse transmitted pulse after

23. before after Amplitude of Reflected & Transmitted Waves: Heavy to Light When a pulse on the heavy rope reaches the interface, the light rope offers little resistance. The light rope is greatly affected by the heavy rope, so the transmitted pulse has a greater amplitude. The upright reflected pulse’s amplitude diminishes since some of the heavy rope’s energy it transmitted to the light rope. incident pulse upright reflected pulse transmitted pulse

24. Refraction • We’ve seen that when a wave reaches an interface (a change from one medium to another), part of the wave can be transmitted, and part can be reflected back. • A rope is a 1-dimensional medium; in a 2-dimensional medium a transmitted wave can change direction. • Refraction - the bending of a wave as it passes from one medium to another • Exp. light bending as it passes from air to glass or water • As ocean waves approach the shore at an angle, the part of the wave closer to shore begins to slow down because the water is shallower. This causes refraction, and the waves bend so that it the wave fronts (crests) come in nearly parallel with the shore. Even though the medium (water) doesn’t change, one of its properties does—the speed of the wave. https://www.youtube.com/watch?v=jQDRNb-E-cY

25. Refraction of Ocean Waves Wave fronts are shown in white heading toward the beach. The water gets shallow at the bottom first, which causes the waves to slow down and bend, and the wavelength to decrease. By the time the waves reach shore, they’re nearly parallel to the shoreline. The effect can even be seen on islands, where winds nearly wrap around it and come toward the island from all sides.

26. Diffraction • When waves bounce off a barrier, this is reflection. When waves bend due to a change in the medium, this is refraction. When waves change direction as they pass around a barrier or through a small opening, this is diffraction. Refraction involves a change in wave speed and wavelength; diffraction doesn’t. • Diffraction- happens as waves bend around a boat in a harbor • This is different than the refraction of waves near shore because the depth of water does not decrease around the boat like it does near shore. • Diffraction is most noticeable when the wavelength is large compared to the obstacle or opening. Thus, no noticeable diffraction may occur if the boat in the harbor is very big.

27. Diffraction Pics When waves pass a barrier they curve around it slightly. When they pass through a small opening, they spread out almost as if they had come from a point source. These effects happen for any type of wave: water; sound; light; seismic waves, etc.

28. Diffraction & Bats • Bats use ultrasonic sound waves (a frequency too high for humans to hear) to hunt moths. The reason they use ultrasound is because at lower frequencies much of the sound waves would have a wavelength close to the size of a moth, which means much of the sound would diffract around it. • Bats hunt by echolocation- bouncing sound waves off of prey and listening for the echoes • so they need to emit sound with a wavelength smaller that the typical moth, which means a high frequency is required. • High frequency sound waves reflect off the moths rather than diffracting around them. If bats hunted bigger prey, we might have emitted sounds that we could hear.

29. Constructive & Destructive Interference Destructive Interference Waves are “out of phase.” By superposition, red and blue completely cancel each other out, if their amplitudes and frequencies are the same. Constructive Interference Waves are “in phase.” By super-position, red + blue = green. If red and blue each have amplitude A, then green has amplitude 2A.

30. Interference Like force vectors, waves can work together or opposition. Sometimes they can even do some of both at the same time. Constructive interference occurs at a point when two waves have displacements in the same direction. The amplitude of the combo wave is larger either individual wave. Destructive interference occurs at a point when two waves have displacements in opposite directions. The amplitude of the combo wave is smaller than that of the wave biggest wave. https://www.youtube.com/watch?v=X8kxKFew_DI

31. Standing Waves When waves on a rope hits a fixed end, it reflects and is inverted. These reflected waves then combine with oncoming incident waves. At certain frequencies the resulting superposition yields a standing wave, in which some points on the rope called nodes never move at all, and other points called antinodes have an amplitude twice as big as the original wave.

32. Waves: What Are They? A wave is a travelling condition or disturbance. Energy travels from one place to another by means of a wave. Transverse wave: disturbance is perpendicular to travel direction. Longitudinal wave: disturbance is parallel to travel direction.

33. Periodic Waves If the source of the disturbance produces it repeatedly, at equal time intervals, the resulting wave is called periodic. Like anything else periodic, these waves are characterized by an amplitude, a period, and a frequency.

34. Periodic Waves Amplitude: maximum magnitude of disturbance Period: time required for one complete cycle Wavelength: distance required for one complete cycle Frequency: number of cycles per second of time

35. Periodic Waves Relationships:

36. Sound Sound is a longitudinal wave in which the disturbance is a change in the pressure in the air (or other medium).

37. Sound Like any wave, sound is characterized by a velocity and a wavelength.

38. Sound As with any wave, the disturbance travels, and energy travels, but the material (air) “sloshes back and forth” mostly in one place.

39. Sound: Speed The speed of a sound wave depends on the mechanical properties of the material through which it moves. Gas: Liquid: Solid:

40. Sound: Energetics The energy carried by a sound wave per second is its power: Power has SI units of J/s = W (watts)

41. Sound: Energetics We define the intensity of a sound wave as the power it carries perpendicularly through a surface, divided by the area of the surface: Intensity has SI units of W/m2. Intensity decreases from surface 1 to surface 2.

42. The Doppler Effect The Doppler Effect is the change in observed frequency of a sound wave (other sorts of waves, too) because of the movement of either the source, or the observer, or both, relative to the air through which the sound is traveling.

43. The Doppler Effect The Doppler Effect is the change in observed frequency of a sound wave (other sorts of waves, too) because of the movement of either the source, or the observer, or both, relative to the air through which the sound is traveling. The observer’s motion causes him to intercept more waves per second than he would if he were standing still.