Chapter 6 Waves and Sound ( Section 2)

1. Chapter 6Waves and Sound(Section 2)

2. 6.2 Aspects of Wave Propagation • In this section, we consider what waves do as they travel. • For waves traveling along a surface or throughout space in three dimensions, it is convenient to use two different ways to represent the wave. • We will call these the wave-front model and the ray model.

3. 6.2 Aspects of Wave Propagation • The figure shows how each is used to illustrate a wave pulse on water as it travels from the point where it was produced. • The wave front is a circle that shows the location of the peak of the wave pulse.

4. 6.2 Aspects of Wave Propagation • A ray is a straight arrow that shows the direction a given segment of the wave is traveling.

5. 6.2 Aspects of Wave Propagation • A laser beam and sunlight passing through a small hole in a window shade both approximate individual rays of light that we can see if there is dust in the air.

6. 6.2 Aspects of Wave Propagation • On the other hand, the rays of water ripples are not visible, but we do see the wave fronts.

7. 6.2 Aspects of Wave Propagation • For a continuous water wave, the wave fronts are concentric circles around the point of origin (the “source” of the wave) that represent individual peaks of the wave.

8. 6.2 Aspects of Wave Propagation • The largest circle shows the position of the first peak that was produced. • Each successive wave front is smaller because it came later and has not traveled as far. • The distance between adjacent wave fronts is equal to the wavelength of the wave.

9. 6.2 Aspects of Wave Propagation • Again, a continuous wave is like a series of wave pulses produced one after another. • The rays used to represent a continuous wave are lines radiating from the source of the wave (the blue arrows in the figure).

10. 6.2 Aspects of Wave Propagation • The wave fronts arriving at a point far from the source are nearly straight lines (far right in the figure). • The corresponding rays are nearly parallel.

11. 6.2 Aspects of Wave Propagation • For a wave moving in three-dimensional space, like the sound traveling outward from you in all directions as you shout or whistle, the wave fronts are spherical shells surrounding the source of the wave. • The wave front of a wave pulse, such as the sound from a hand clap, expands like a balloon that is being inflated very rapidly.

12. 6.2 Aspects of Wave Propagation • For continuous three-dimensional waves such as a steady whistle, the wave fronts form a series of concentric spherical shells that expand like the circular wave fronts of a wave on a surface. • A 440-hertz tuning fork produces 440 of these wave fronts each second. • The surface of each wave front expands outward with a speed of 344 m/s (at room temperature). • As with waves on a surface, the rays used to represent a continuous wave in three dimensions are lines radiating outward from the wave source.

13. 6.2 Aspects of Wave Propagation • One inherent aspect of the propagation of waves on a surface or in three dimensions is that the amplitude of the wave necessarily decreases as the wave gets farther from the source. • A certain amount of energy is expended to create a wave pulse or each cycle of a continuous wave.

14. 6.2 Aspects of Wave Propagation • This energy is distributed over the wave front and determines the amplitude of the wave: • The greater the amount of energy given to a wave front, the larger the amplitude. • As the wave front moves out, it gets larger, so this energy is spread out more and becomes less concentrated. • This attenuation accounts for the decrease in loudness of sound as a noisy car moves away from you and for the decrease in brightness of a lightbulb as you move away from it.

15. 6.2 Aspects of Wave Propagation • One can infer when the amplitude of a wave is changing by noting changes in the wave front or the rays. If the wave fronts are growing larger, then the amplitude is getting smaller. • The same thing is indicated when the rays are diverging (slanting away from each other).

16. 6.2 Aspects of Wave Propagation • At great distances from the source of a three-dimensional wave, the wave fronts become nearly flat and are called plane waves. • The corresponding rays are parallel, and the wave’s amplitude stays constant. • The light and other radiation we receive from the Sun come as plane waves because of the great distance between Earth and the Sun. • With this background, we will look at several phenomena associated with wave propagation.

17. 6.2 Aspects of Wave PropagationReflection • A wave is reflected whenever it reaches a boundary of its medium or encounters an abrupt change in the properties (density, temperature, and so on) of its medium. • A wave pulse traveling on a rope is reflected when it reaches a fixed end.

18. 6.2 Aspects of Wave PropagationReflection • It “bounces” off the end and travels back along the rope. • Notice that the reflected pulse is inverted. • When the end of the rope is attached to a very light (but strong) string instead, the reflected pulse is not inverted.

19. 6.2 Aspects of Wave PropagationReflection • The incoming pulse causes two pulses to leave the junction, a reflected pulse and a pulse that continues into the light string. • This reflection occurs because of an abrupt change in the density of the medium from high density (for the heavy rope) to low density (for the light string).

20. 6.2 Aspects of Wave PropagationReflection • Similarly, a wave on a surface or a wave in three dimensions is reflected when it encounters a boundary. • The wave that “bounces back” is called the reflected wave. • Rays are more commonly used to illustrate reflection because they nicely show how the direction of each part of the wave is changed.

21. 6.2 Aspects of Wave PropagationReflection • When a wave is reflected from a straight boundary (for surface waves) or a flat boundary (in three dimensions), the reflected wave appears to be expanding out from a point behind the boundary.

22. 6.2 Aspects of Wave PropagationReflection • This point is called the image of the original wave source. • An echo is a good example: sound that encounters a large flat surface, such as the face of a cliff, is reflected and sounds like it is coming from a point behind the cliff.

23. 6.2 Aspects of Wave PropagationReflection • Our most common experience with reflection is that of light from a mirror. • The image that you see in a mirror is a collection of reflected light rays originating from the different points on the object you see.

24. 6.2 Aspects of Wave PropagationReflection • Reflection from surfaces that are not flat (or straight) can cause interesting things to happen to waves. • The figure shows a wave being reflected by a curved surface. • Note that the rays representing the reflected part of the wave are converging toward each other.

25. 6.2 Aspects of Wave PropagationReflection • This means that the amplitude of the wave is increasing—the wave is being “focused.” • Parabolic microphones seen on the sidelines of televised football games use this principle to reinforce the sounds made on the playing field. • Satellite receiving dishes do the same with radio waves.

26. 6.2 Aspects of Wave PropagationReflection • A reflector in the shape of an ellipse has a useful property. • Recall that the orbits of satellites, comets, and planets can be ellipses. • An ellipse has two points in its interior called foci (the plural of focus). • If a wave is produced at one focus, it will converge on the other focus after reflecting off the elliptical surface. • All rays originating from one focus reflect off the ellipse and pass through the other focus.

27. 6.2 Aspects of Wave PropagationReflection • A room shaped like an ellipse is called a whispering chamber because a person standing at one focus can hear faint sounds—even whispering—produced at the other focus. • This property of the ellipse is also used in the medical treatment of kidney stones.

28. 6.2 Aspects of Wave PropagationDoppler Effect • Can you recall the last time a fast-moving emergency vehicle with its siren blaring passed near you? • If so, you may remember that the pitch or tone of its sound dropped suddenly as it went by— • Although, you may be so used to this phenomenon that you didn’t notice it.

29. 6.2 Aspects of Wave PropagationDoppler Effect • This is a manifestation of the Doppler effect: • The apparent change in the frequency of wave fronts emitted by a moving source, perhaps a tugboat floating down a river or a train traveling along a track, each blowing its horn. • Each wave front expands outward from the point where the source was when it emitted that wave front.

30. 6.2 Aspects of Wave PropagationDoppler Effect • In contrast to what is shown in the figure, where the source is stationary, ahead of the moving source, the wave fronts are bunched together.

31. 6.2 Aspects of Wave PropagationDoppler Effect • This means that the wavelength is shorter than when the source is at rest, and therefore the frequency of the wave is higher. • Behind the moving source, the wave fronts are spread apart: • The wavelength is longer, and the frequency is lowerthan when the source is motionless.

32. 6.2 Aspects of Wave PropagationDoppler Effect • In both places, the higher the speed of the wave source, the greater the change in frequency. • Note: The speed of a wave in a medium is constant and is not affected by any motion associated with the wave source. • Thus, if the wavelength goes up, the frequency must go down, and vice versa, to yield a constant wave speed: v = lf

33. 6.2 Aspects of Wave PropagationDoppler Effect • The frequency of sound that reaches a person in front of a moving train is higher than that perceived when the train is not moving. • A person behind the moving train hears a lower frequency. • As a train or a fast car moves by, you hear the sound shift from a higherfrequency (pitch) to a lower frequency. • The change in the loudness of the sound, which you also hear, is not part of the Doppler effect: • it involves a separate process

34. 6.2 Aspects of Wave PropagationDoppler Effect • A similar shift in frequency of sound occurs if you are moving toward a stationary sound source.

35. 6.2 Aspects of Wave PropagationDoppler Effect • This Doppler shift happens because the speed of the wave relative to you is higher than that when you are not moving. • The wave fronts approach you with a speed equal to the wave speed plus your speed. • Because the wavelength is not affected, the equation v =fl tells us that the frequency of the wave is increased in proportion to the speed of the wave relative to you. • By the same reasoning, when one is moving away from the sound source, the frequency is reduced.

36. 6.2 Aspects of Wave PropagationDoppler Effect • The Doppler effect occurs for both sound and light and is routinely taken into account by astronomers. • The frequencies of light emitted by stars that are moving toward or away from Earth are shifted. • If the speed of the star is known, the original frequencies of the light can be computed. • If the frequencies are known instead, the speed of the star can be computed from the amount of the Doppler shift. • Such information is essential for determining the motions of stars in our galaxy or of entire galaxies throughout the universe.

37. 6.2 Aspects of Wave PropagationDoppler Effect • Echolocation is the process of using the waves reflected from an object to determine its location. Radar and sonar are two examples. • Basic echolocation uses reflection only: • A wave is emitted from a point, reflected by an object of some kind, and detected on its return to the original point. • The time between the emission of the wave and the detection of the reflected wave (the round-trip time) depends on the speed of the wave and the distance to the reflecting object.

38. 6.2 Aspects of Wave PropagationDoppler Effect • For example, if you shout at a cliff and hear the echo 1 second later, you know that the cliff is approximately 172 meters away. • This is because the sound travels a total of 344 meters (172 meters each way) in 1 second (at room temperature). • If it takes 2 seconds, the cliff is approximately 344 meters away, and so on.

39. 6.2 Aspects of Wave PropagationDoppler Effect • With sonar, a sound pulse is emitted from an underwater speaker, and any reflected sound is detected by an underwater microphone. • The time between the transmission of the pulse and the reception of the reflected pulse is used to determine the distance to the reflecting object. • Basic radar uses a similar process with microwaves that reflect off aircraft, raindrops, and other things.

40. 6.2 Aspects of Wave PropagationDoppler Effect • Incorporating the Doppler effect in echolocation makes it possible to immediately determine the speed of an approaching or departing object. • A moving object causes the reflected wave to be Doppler shifted. • If the frequency of the reflected wave is higher than that of the original wave, the object is moving toward the source. • If the frequency is lower, then the object is moving away.

41. 6.2 Aspects of Wave PropagationDoppler Effect • Doppler radar uses this combination of echolocation and the Doppler effect. • The time between transmission and reception gives the distance to the object, whereas the amount of frequency shift is used to determine the speed. • Law-enforcement officers use Doppler radar to check the speeds of vehicles, and Doppler radar is also used in base-ball, tennis, and other sports to clock the speed of a ball.

42. 6.2 Aspects of Wave PropagationDoppler Effect • Dust, raindrops, and other particles in air reflect microwaves, making it possible to detect the rapidly swirling air in a tornado with Doppler radar. • Another potentially life-saving application is the detection of wind shear—drastic changes in wind speed near storms that have caused low-flying aircraft to crash.

43. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • In the previous discussion, we have implicitly assumed that the speed of the wave source is much less than the wave speed itself. • However, if you’ve ever heard a sonic boom or been jostled by the wake of a passing watercraft while floating in the water, you’ve had experience with circumstances where the reverse is true.

44. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • The figure shows another series of wave fronts produced by a moving wave source. • This time the speed of the wave source is greater than the wave speed. • The wave fronts “pile up” in the forward direction and form a large-amplitude wave pulse called a shock wave. • This is what causes the V-shaped bow waves produced by swimming duck and moving boats.

45. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • Aircraft flying faster than the speed of sound produce a similar shock wave. • In this case, the three-dimensional wave fronts form a conical shock wave, with the aircraft at the cone’s apex. • This conical wave front moves with the aircraft and is heard as a sonic boom (a sound pulse) by persons on the ground.

46. 6.2 Aspects of Wave PropagationDiffraction • Think about walking down a street and passing by an open door or window with sound coming from inside. • You can hear the sound even before you get to the opening, as well as after you’ve passed it. • The sound doesn’t just go straight out of the opening like a beam, it spreads out to the sides. • This is diffraction.

47. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • The figure shows wave fronts as they reach a gap in a barrier. • These might be sound waves passing through a door or ocean waves encountering a breakwater. • The part of the wave that passes through the gap actually sends out wave fronts to the sides as well as ahead. • The rays that represent this process show that the wave “bends” around the edges of the opening.

48. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • The extent to which the diffracted wave spreads out depends on the ratio of the size of the opening to the wavelength of the wave. • When the opening is much larger than the wavelength, there is little diffraction: • The wave fronts remain straight and do not spread out to the sides appreciably. • This is what happens when light comes in through a window. • The wavelength of light is less than a millionth of a meter, and consequently, there is little diffraction.

49. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • When the wavelength is roughly the same size as the opening, the diffracted wave spreads out much more.

50. 6.2 Aspects of Wave PropagationBow Waves and Shock Waves • The sizes of windows and doors are well within the range of the wavelengths of sound waves, so sound diffracts a great deal after passing through them. • Higher frequencies (shorter wavelengths) are not diffracted as much as the lower frequencies.