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The Doppler Effect B A is an apparent(observed) change in frequency and wavelength of a wave occurring when the source and observer are in motion relative to each other, with the perceived frequency increasing when the source and observer approach each other and decreasing when they move apart. WHY? Let A and B be two stationary observers. Consider first stationary source (student tapping a desk at a constant pace) : The crests move away from the source at a constant speed. The distance between adjacent crests is one wavelength and is the same toward observer A as toward observer B. The freq of waves reaching both observes is the same and equal to the freq of a wave as it leaves its source.
A B Now: source moves to the right at speed < wave speed. Each new wave originates from the point farther to the right. First wavereaches A and B at the same time. 2nd , 3rd , 4th ,.. wave reaches B sooner than it reaches A. B sees waves coming more frequently i.e. B observes higher frequency and shorter wavelength. Similarly, A observes lower frequency and longer wavelength. General: If the source and the listener are approaching each other the perceived frequency is higher: if they are moving apart, the perceived frequency is lower.
If a source of sound is moving toward you at constant speed, you hear a higher freq than when it is at rest • If it is moving at increasing speed you hear higher and higher freq • If a source of sound is moving away from you, you hear a lower freq than when it is at rest • If it is moving at increasing speed you hear lower and lower freq • You can hear this effect with sirens on fire engines of train whistles • A similar effect occurs with light waves and radar waves
Applications The Doppler effect is the basis of a technique used to measure the speed of flow of blood. Ultrasound (high-frequency sound waves) are directed into an artery. The waves are reflected by blood cells back to a receiver. The frequency detected at the receiver fr relative to that emitted by the source f indicates the cell’s speed and the speed of the blood. Applications: A similar arrangement is used to measure the speed of cars, but microwaves (EM waves) are used instead of ultrasound.
Doppler effect Radar guns When radar waves bounce off a moving object (echo ) the frequency of the reflected wave changes by an amount that depends on how fast the object is moving. The detector senses the frequency shift and translates this into a speed. http://auto.howstuffworks.com/radar-detector1.htm
Light or in general EM wave is a wave. Doppler effect is the characteristic of these waves too. Based on calculations using the Doppler effect, it appears that nearby galaxies are moving away from us at speed of about 250,000 m/s. The distant galaxies are moving away at speeds up to 90 percent the speed of light. The universe is moving apart and expanding in all directions.
Astronomy: the velocities of distant galaxies can be determined from the Doppler shift. Freqs. of EM waves coming from stars are very often lower than those obtained in the laboratory emitted from same elements (He, H). Redshift – shift toward lower freq. Red light has the lowest frequency out of all of the visible lights. Most distant galaxies are observed to be red-shifted in the color of their light, which indicates that they are moving away from the Earth. Some galaxies, however, are moving toward us, and their light shows a blue shift. Edwin Hubble discovered the Redshift in the 1920's. His discovery led to him formulating the Big Bang Theory of the Universe's origin.
A science teacher demonstrating the Doppler effect
We now look to see what happens to a wave when it is incident on the boundary between two media. When a wave strikes a boundary between two media some of it is reflected, some is absorbed and some of it is transmitted. How much of each? That depends on the media and the wave itself.
Reflection of Waves All waves can be reflected.
fixed end First of all, we shall look at a single pulse travelling along a string. The end of the rope if fixed – reflected pulse returns inverted. the pulse has undergone a 180° (π) phase change. Some of the energy of the pulse will actually be absorbed at the support and as such, the amplitude of the reflected pulse will be less than that of the incident pulse (E ~ A2). Free end – reflected pulse is not inverted. there is no phase change. Imagine whip
i = r. Law of Reflection The incident and reflected wavefronts. Angle of reflection is equal to angle of incidence. (the angles are measured to the normal to the barrier). All waves, including light, sound, water obey this relationship, the law of reflection.
Refraction When a wave passes from one medium to another, its velocity changes. The change in speed results in a change in direction of propagation of the refracted wave.
When a wave passes from one medium to another, its velocity changes. The change in speed results in a change in direction of propagation of the refracted wave. Visualization of refraction As a toy car rolls from a hardwood floor onto carpet, it changes direction because the wheel that hits the carpet first is slowed down first.
The incident and refracted wavefronts. light waves sound waves frequency is determined by the source so it doesn’t change. Only wavelenght changes. Wavelength of the same wave is smaller in the medium with smaller speed.
A mathematical law which will tell us exactly HOW MUCH the direction has changed is calledSNELL'S LAW. Although it can be derived by using little geometry and algebra, it was introduced as experimental law for light in 1621. For a given pair of media, the ratio θ1 is constant for the given frequency. The Snell’s law is of course valid for all types of waves. θ2
www.le.ac.uk/ua/mjm33/wave2/images/Snell.gif Refraction occurs when a wave enters a medium with different speed of wave. When the wave enters a medium with slower speed the wavelength becomes shorter and the wave speed decreases. The frequency remains the same.
The speed of light inside matter • The speed of light c = 300,000,000 m/s = 3 x 108 m/s • In any other medium such as water or glass, light travels at a lower speed. • INDEX OF REFRACTION, n,of the medium is the ratio of the speed of light in a vacuum, c, and the speed of light, v, in that medium: • no units • As c is greater than v for all media, n will always be > 1. • greater n – smaller speed of light in the medium. • As the speed of light in air is almost equal to c, nair ~ 1
Refraction of light Incident ray refracted ray Water n= 1.33 Glass (n=1.5) The refracted ray is refracted more in the glass
SNELL'S LAW Can be written in another form for refraction of light only. greater n ⇒ smaller speed of light ⇒ stronger refraction ⇒ smaller angle
Which of the three drawings (if any) show physically possible refraction? Answer: (a) refraction toward normal as it should be
Dispersion Even though all colors of the visible spectrum travel with the same speed in vacuum, the speed of the colors of the visible spectrum varies when they pass through a transparent medium like glass and water. That is, the refractive index of glass is different for different colours. Different colors are refracted by different amounts. White light contains all wavelengths (colors) Red Orange Yellow Green Blue Indigo Violet
Total internal reflection n2 q2=900 qc n1 Angle of refraction is greater than angle of incidence. As the angle of incidence increases, so does angle of refraction. The intensity of refracted light decreases, intensity of reflected light increases until angle of incidence is such that angle of refraction is 900. Critical angle: qc -angle of incidence for whichangle of refraction is 900 When the incident angle is greater than qc, the refracted ray disappears and the incident ray is totally reflected back.
Critical angle: qc -angle of incidence for whichangle of refraction is 900
A Smile in the Sky • Rainbows are caused by dispersion of sunlight by water droplets 1. When white sunlight enters droplet its component colors are refracted at different angles (dispersion) 2. These colored lights then undergo total internal reflection. observer is between the Sun and a rain shower. 3. Second refraction from droplet into air – more dispersion 4. Each droplet produces a complete spectrum, but only one from eachis seen by observer – you have your own personal rainbow and I have MINE!
A gemstone's brilliance is caused by total internal reflection A gemstone's"fire" is caused by dispersion Maximize brilliance & fire by knowing physics
What does it mean to “see” something? • To “see” something, light rays from the object must get into your eyes. • unless the object if a light bulb or some other luminous object, the light rays from some light source (like the sun) reflect off of the object and enter our eyes. (root)BEER!
Where is the fish? Deeper than you think! Apparent location of the fish
Is the straw really broken? refracted ray perceived straw incident ray real straw
Where is the ball? Closer than you think! Apparent location of the ball ball
It looks like a moon setting over a body of water, with the moon's reflection in the surface. We can even see floating leaves on the water's surface. That is not what this picture is. Instead we are looking at a light in the swimming pool, and the light's reflection on the surface of the water.
A fish’s eye view result of total internal reflection Looking upward from beneath the water a person would see the outside world squeezed into a into a cone with an angle of 980.
MIRAGES Formation of mirages: On a hot day (dessert – every day is hot) there is a layer of very hot air just above the ground. There are actually layers of less and less hot air farther above the surface. Hot air is less dense then the cooler air. The light of the distant object originally slanted downward is refracted away from the normal at every interface between two layers of different density until eventually the angle of incidence is greater then the critical angle for interface between two layers of different densities. cooler hot A mirage is caused not by a loss of mental facility on a hot, dry dessert, but by refracted light that appears to be reflected from the smooth surface of a pond in front of an object which is image of the sky.
So, when you see something that appears to be a wet spot on a distant part of a hot highway, you are OK. This is just light that originates in the sky and travels toward the highway. Before reaching the pavement, it is bent, reflected and then again refracted up into your eye by the hot air above the road. You are seeing light from the blue sky.
Fiber optics Click me A fiber optic cable is a bunch (thousandths) of very fine (less than the diameter of a hair) glass strands clad together made of material with high index of refraction. Critical angle isvery small almost everything is totally internally reflected. The light is guided through the cable by successive internal reflections with almost no loss (a little escapes). Trick is in sending the light at just right angle initially. Even if the light pipe is bent into a complicated shape (tied into knots), light is transmitted practically undiminished to the other end.
fiber optic communications • can carry more info with less distortion over long distances • not affected by atmospheric conditions or lightning and does not corrode • Used to transmit telephone calls and other communication signals. • One single optical fiber can transmit several TV programs and tens of thousands of telephone conversations, all at the same time. • copper can carry 32 telephone calls, fiber optics can carry 32,000 calls • takes 300 lbs of copper to carry same info as 1 lb of fiber optics • downside expensive Used to illuminate difficult places to reach, such as inside the human body (endoscope – bronchoscope – colonoscope …).
Diffraction When waves pass through a small opening, or pass the edge of a obstacle, they always spread out to some extent into the region that is not directly in the path of the waves. The spreading of a wave into a region behind an obstruction is called diffraction. - into the region of the geometrical shadow
Water waves diffracting through two different sized openings.. The waves are diffracted more through the narrower opening, when wavelength is larger than the opening. diffraction effects are small when slit is much larger than the incident λ. Diffraction by a large object Almost sharp edges – small diffraction around obstacle Diffraction by a small object Strong diffraction effect behind the obstacle remember: big wavelength big diffraction effects
For example, if two rooms are connected by an open doorway and a sound is produced in a remote corner of one of them, a person in the other room will hear the sound as if it originated at the doorway. Diffraction provides the reason why we can hear something even if we can not see it. Lower-frequency (longer-wavelength) waves can diffract around larger obstacles, while high-frequency waves are simply stopped by the same obstacles. This is why AM radio waves (~1 MHz, 300 m wavelength) signals can diffract around a building, mountain still producing a usable signal on the other side, while FM (~100 MHz, 3 m wavelength) signals essentially require a line-of-sight path between transmitter and receiver.
Ultrasound is used for echolocation: dolphins, bats, sonar, sonograms Sonar appeared in the animal kingdom long before it was developed by human engineers. But why ultrasound? Because of diffraction!!! Or should we say because of no difraction!!! Low frequency sound has longer wavelength, so they will be diffracted, so not being able to detect the prey. High frequency sound has smaller wavelength, so it will be reflected back from the prey. That’s how bat “sees” its prey. So when ultrasound is emitted toward obstacle it will be reflected back rather then spread behind the obstacle. dolphins, ocras, whales
To echolocate an object one must have both emitter and detector. If the wavelength of an emitted wave is smaller than the obstacle which it encounters, the wave is not able to diffract around the obstacle, instead the wave reflects off the obstacle. Reflected wave is caught by detector giving it information on how far (2d = vt) and how big is the object (reflection from different directions) The ultrasound bats typically chirp is ~ 50 000 Hz. What is wavelength of that sound? The speed of sound wave in air is ~ 340 m/s. v = lf so l = v/f l = 0.0068 m = 0.7 cm So, bats use ultrasonic waves with l smaller than the dimensions of their prey (moth – couple of centimeters).
Keep in mind that wavelengths of the audible sound are < 1m, of the visible light ~ 10-7 m, and water waves you can see for yourself. Now you can understand that diffraction in the case of sound or water can be very obvious, but for light is not so. Light waves (red light: λ ~ 500 nm = 0.0005 mm) do not diffract very much. Obstacle should be very small. a Shadow!!! (No light behind the obstacle!)
2. Suggest one reason why ships at sea use a very low frequency sound for their foghorn. And low frequency sounds do propagate much further than high-frequency ones – due to diffraction. EXAMPLE Another reason and maybe even better explanation is that the method of generating the sound involves the production of a very strong pressure pulse. The fog horn is loud so that it can be heard far away. Elephants also use these deep sounds to communicate over long distance.
Interference - Superposition two objects can not be at the same place at the same time! but two waves can be at the same place at the same time! and when they meet they interfere, superimpose and then carry on living happily ever after as they never met each other Property that distinguishes waves from particles: waves can superpose when overlapping and as the result a lot of possible craziness can happen.
