Under the right conditions humid air and low frequency , a sound wave in a straight pipe could theoretically travel hundreds of kilometers before being noticeable attenuated. In general, the absorption of mechanical waves depends a great deal on the chemical composition and microscopic structure of the medium. Ripples on the surface of antifreeze, for instance, die out extremely rapidly compared to ripples on water.
For sound waves and surface waves in liquids and gases, what matters is the viscosity of the substance, i. This explains why our intuitive expectation of strong absorption of sound in water is incorrect. Water is a very weak absorber of sound viz. Light is an interesting case, since although it can travel through matter, it is not itself a vibration of any material substance. The Hubble Space Telescope routinely observes light that has been on its way to us since the early history of the universe, billions of years ago.
Of course the energy of light can be dissipated if it does pass through matter and the light from distant galaxies is often absorbed if there happen to be clouds of gas or dust in between.
Typical amateur musicians setting out to soundproof their garages tend to think that they should simply cover the walls with the densest possible substance. In fact, sound is not absorbed very strongly even by passing through several inches of wood. A better strategy for soundproofing is to create a sandwich of alternating layers of materials in which the speed of sound is very different, to encourage reflection. The classic design is alternating layers of fiberglass and plywood.
The speed of sound in plywood is very high, due to its stiffness, while its speed in fiberglass is essentially the same as its speed in air. Both materials are fairly good sound absorbers, but sound waves passing through a few inches of them are still not going to be absorbed sufficiently.
The point of combining them is that a sound wave that tries to get out will be strongly reflected at each of the fiberglass-plywood boundaries, and will bounce back and forth many times like a ping pong ball. Due to all the back-and-forth motion, the sound may end up traveling a total distance equal to ten times the actual thickness of the soundproofing before it escapes.
This is the equivalent of having ten times the thickness of sound-absorbing material. A radio transmitting station must have a length of wire or cable connecting the amplifier to the antenna. The cable and the antenna act as two different media for radio waves, and there will therefore be partial reflection of the waves as they come from the cable to the antenna. If the waves bounce back and forth many times between the amplifier and the antenna, a great deal of their energy will be absorbed.
There are two ways to attack the problem. One possibility is to design the antenna so that the speed of the waves in it is as close as possible to the speed of the waves in the cable; this minimizes the amount of reflection. The other method is to connect the amplifier to the antenna using a type of wire or cable that does not strongly absorb the waves. Partial reflection then becomes irrelevant, since all the wave energy will eventually exit through the antenna.
How would its energy and frequency compare with those of the original sound? Would it sound any different? What happens if you swap the two wires where they connect to a stereo speaker, resulting in waves that vibrate in the opposite way? In this subsection we analyze the reasons why reflections occur at a speed-changing boundary, predict quantitatively the intensities of reflection and transmission, and discuss how to predict for any type of wave which reflections are inverting and which are uninverting.
To understand the fundamental reasons for what does occur at the boundary between media, let's first discuss what doesn't happen. For the sake of concreteness, consider a sinusoidal wave on a string. A change in frequency without a change in wavelength would produce a discontinuity in the wave. A simple change in wavelength without a reflection would result in a sharp kink in the wave.
The sudden change in the shape of the wave has resulted in a sharp kink at the boundary. This can't really happen, because the medium tends to accelerate in such a way as to eliminate curvature.
A sharp kink corresponds to an infinite curvature at one point, which would produce an infinite acceleration, which would not be consistent with the smooth pattern of wave motion envisioned in fig. Waves can have kinks, but not stationary kinks. We conclude that without positing partial reflection of the wave, we cannot simultaneously satisfy the requirements of 1 continuity of the wave, and 2 no sudden changes in the slope of the wave.
In other words, we assume that both the wave and its derivative are continuous functions. Does this amount to a proof that reflection occurs? Not quite. We have only proved that certain types of wave motion are not valid solutions. In the following subsection, we prove that a valid solution can always be found in which a reflection occurs.
Now in physics, we normally assume but seldom prove formally that the equations of motion have a unique solution, since otherwise a given set of initial conditions could lead to different behavior later on, but the Newtonian universe is supposed to be deterministic. Since the solution must be unique, and we derive below a valid solution involving a reflected pulse, we will have ended up with what amounts to a proof of reflection. I will now show, in the case of waves on a string, that it is possible to satisfy the physical requirements given above by constructing a reflected wave, and as a bonus this will produce an equation for the proportions of reflection and transmission and a prediction as to which conditions will lead to inverted and which to uninverted reflection.
We assume only that the principle of superposition holds, which is a good approximations for waves on a string of sufficiently small amplitude. The top drawing shows the pulse heading to the right, toward the heaver string. For clarity, all but the first and last drawings are schematic. Once the reflected pulse begins to emerge from the boundary, it adds together with the trailing parts of the incident pulse.
Their sum, shown as a wider line, is what is actually observed. We can without loss of generality take the incident original wave to have unit amplitude. To avoid a discontinuity, we must have. Next we turn to the requirement of equal slopes on both sides of the boundary. Let the slope of the incoming wave be s immediately to the left of the junction. If, for example, the wave speed is twice as great on the right side, then the slope is cut in half by this effect.
The first equation shows that there is no reflection unless the two wave speeds are different, and that the reflection is inverted in reflection back into a fast medium. The energies of the transmitted and reflected wavers always add up to the same as the energy of the original wave. There is never any abrupt loss or gain in energy when a wave crosses a boundary; conversion of wave energy to heat occurs for many types of waves, but it occurs throughout the medium. This does not violate conservation of energy, because this occurs when the second string is less massive, reducing its kinetic energy, and the transmitted pulse is broader and less strongly curved, which lessens its potential energy.
For waves on a string, reflections back into a faster medium are inverted, while those back into a slower medium are uninverted. Is this true for all types of waves? The rather subtle answer is that it depends on what property of the wave you are discussing. Let's start by considering wave disturbances of freeway traffic.
Anyone who has driven frequently on crowded freeways has observed the phenomenon in which one driver taps the brakes, starting a chain reaction that travels backward down the freeway as each person in turn exercises caution in order to avoid rear-ending anyone. The reason why this type of wave is relevant is that it gives a simple, easily visualized example of how our description of a wave depends on which aspect of the wave we have in mind.
In steadily flowing freeway traffic, both the density of cars and their velocity are constant all along the road. Since there is no disturbance in this pattern of constant velocity and density, we say that there is no wave. Now if a wave is touched off by a person tapping the brakes, we can either describe it as a region of high density or as a region of decreasing velocity. The freeway traffic wave is in fact a good model of a sound wave, and a sound wave can likewise be described either by the density or pressure of the air or by its speed.
Likewise many other types of waves can be described by either of two functions, one of which is often the derivative of the other with respect to position. Now let's consider reflections. If we observe the freeway wave in a mirror, the high-density area will still appear high in density, but velocity in the opposite direction will now be described by a negative number.
Although I don't know any physical situation that would correspond to the reflection of a traffic wave, we can immediately apply the same reasoning to sound waves, which often do get reflected, and determine that a reflection can either be density-inverting and velocity-uninverting or density-uninverting and velocity-inverting.
This same type of situation will occur over and over as one encounters new types of waves, and to apply the analogy we need only determine which quantities, like velocity, become negated in a mirror image and which, like density, stay the same.
A light wave, for instance, consists of a traveling pattern of electric and magnetic fields. All you need to know in order to analyze the reflection of light waves is how electric and magnetic fields behave under reflection; you don't need to know any of the detailed physics of electricity and magnetism.
An electric field can be detected, for example, by the way one's hair stands on end. The direction of the hair indicates the direction of the electric field. In a mirror image, the hair points the other way, so the electric field is apparently reversed in a mirror image. The behavior of magnetic fields, however, is a little tricky. The magnetic properties of a bar magnet, for instance, are caused by the aligned rotation of the outermost orbiting electrons of the atoms.
In a mirror image, the direction of rotation is reversed, say from clockwise to counterclockwise, and so the magnetic field is reversed twice: once simply because the whole picture is flipped and once because of the reversed rotation of the electrons.
In other words, magnetic fields do not reverse themselves in a mirror image. We can thus predict that there will be two possible types of reflection of light waves.
In one, the electric field is inverted and the magnetic field uninverted example 23 , p. In the other, the electric field is uninverted and the magnetic field inverted. If you look at the front of a pair of high-quality binoculars, you will notice a greenish-blue coating on the lenses. This is advertised as a coating to prevent reflection. Now reflection is clearly undesirable we want the light to go in the binoculars but so far I've described reflection as an unalterable fact of nature, depending only on the properties of the two wave media.
The coating can't change the speed of light in air or in glass, so how can it work? The key is that the coating itself is a wave medium. In other words, we have a three-layer sandwich of materials: air, coating, and glass. We will analyze the way the coating works, not because optical coatings are an important part of your education but because it provides a good example of the general phenomenon of wave interference effects.
There are two different interfaces between media: an air-coating boundary and a coating-glass boundary. Partial reflection and partial transmission will occur at each boundary. Once more there are several noteworthy characteristics. First, observe that the transmitted pulse is not inverted. In fact inversion only occurs for the reflected pulse if it occurs at all.
Second, observe that the transmitted pulse has a smaller speed and a smaller wavelength than the incident pulse. This is always the case for boundary situations in which a pulse in a less dense medium reflects off the boundary with a more dense medium.
Since wave speeds and wavelengths in strings are always greatest in a least dense medium, it would be expected that there is a decrease in wave speed and wavelength as the pulse crosses the boundary. Finally, when waves cross boundaries the frequency of the incident pulse is the same as the frequency of the transmitted pulse though it is not evident from the above animation.
The fact is that the vibration of the last particle in the incident medium creates the vibration of the first particle on the opposite side of the boundary. These two particles are joined in such a manner that the frequency at which one particle vibrates is equal to the frequency at which the other particle vibrates.
Like two hands shaking with each other, the frequency at which one hand shakes can never be any different that the frequency at which the other hand shakes assuming they remain adjoined to each other. It is this handshake principle that explains why the frequency of the incident pulse and the transmitted pulse must be the same.
For more information on physical descriptions of waves, visit The Physics Classroom Tutorial. If a pulse is introduced at the left end of the rope, it will travel through the rope towards the right end of the medium. This pulse is called the incident pulse since it is incident towards i. The disturbance that returns to the left after bouncing off the pole is known as the reflected pulse. That is, if an upward displaced pulse is incident towards a fixed end boundary, it will reflect and return as a downward displaced pulse.
Similarly, if a downward displaced pulse is incident towards a fixed end boundary, it will reflect and return as an upward displaced pulse. Instead of being securely attached to a lab pole, suppose it is attached to a ring that is loosely fit around the pole. Because the right end of the rope is no longer secured to the pole, the last particle of the rope will be able to move when a disturbance reaches it.
This end of the rope is referred to as a free end. When the incident pulse reaches the end of the medium, the last particle of the rope can no longer interact with the first particle of the pole. Since the rope and pole are no longer attached and interconnected, they will slide past each other.
So when a crest reaches the end of the rope, the last particle of the rope receives the same upward displacement; only now there is no adjoining particle to pull downward upon the last particle of the rope to cause it to be inverted. The result is that the reflected pulse is not inverted. When an upward displaced pulse is incident upon a free end, it returns as an upward displaced pulse after reflection.
And when a downward displaced pulse is incident upon a free end, it returns as a downward displaced pulse after reflection. Inversion is not observed in free end reflection.
Physics 20 Transmission of a Pulse Across a Boundary from Less to More Dense Consider a thin rope attached to a thick rope, with each rope held at opposite ends by people. And suppose that a pulse is introduced by the person holding the end of the thin rope. If this is the case, there will be an incident pulse traveling in the less dense medium the thin rope towards the boundary with a more dense medium the thick rope.
The disturbance that returns to the left after bouncing off the boundary is known as the reflected pulse. The disturbance that continues moving to the right is known as the transmitted pulse. During the interaction between the two media at the boundary, the first particle of the more dense medium overpowers the smaller mass of the last particle of the less dense medium. This causes an upward displaced pulse to become a downward displaced pulse.
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