Ripple Tank Applet Directions
Click here to go to the applet.
This applet is a simulation that demonstrates
scalar waves
in two dimensions. Wave motion crops up in many different areas in
physics; water waves, sound, and light are three examples.
When the applet starts up you will see a
white square (called the "source") emitting circular waves.
The light areas are positive and the dark areas are negative. So, if you
prefer to think of the waves as sound waves, the light areas would be
areas of high
pressure, and the dark areas would be low pressure. The source might be
a speaker of some sort.
You can drag the source around wherever you want. Also you can create new waves (areas of
high pressure) by clicking anywhere. There is a popup menu that
controls what the mouse does. By default it is set to
"Mouse = Draw Wave (+)". Hold down the command or alt key while drawing to freeze the
simulation.
Click the right mouse to bring up a popup menu to add various objects to block the path of the waves. Once you
select one, it will be placed on the screen, and you can draw it anywhere you like, or click and drag the ends of it to
resize it. Right-click on the object to edit its parameters.
The Setup popup can be used to view some interesting
pre-defined experiments. Once an experiment is selected,
you may modify it all you want. The choices are:
- Single Source: this is just a single source emitting circular waves.
- Two Sources: this is just two sources emitting circular waves,
creating an interference pattern between them.
- Four Sources.
- Single Slit: this demonstrates diffraction of waves
travelling through a slit.
- Double Slit: this demonstrates diffraction of waves
travelling through a double slit.
- Triple Slit.
- Obstacle: this demonstrates diffraction of waves
travelling around an obstacle.
- Half Plane: this demonstrates diffraction of waves
around the edge of a plane.
- Dipole Source: this demonstrates an acoustic dipole source consisting of
two sources out of phase.
- Lateral Quadrupole: this demonstrates an acoustic quadrupole source consisting of
four sources arranged in a square.
- Linear Quadrupole: this demonstrates an acoustic quadrupole source consisting of
four sources arranged in a line.
- Hexapole.
- Octupole.
- 12-Pole.
- Plane Wave: this demonstrates a simple plane wave source.
- Intersecting Planes: this demonstrates two plane waves intersecting
at right angles.
- Phased Array 1: this is a group of point
sources arranged in a line, where the relative phases of each point
is different. This causes the radiation to be pointed
downwards. The angle can be adjusted with the Phase Difference
slider.
- Phased Array 2: this is a group of point
sources arranged in a line, where the relative phases of each source
causes the radiation to be directed at a single point. The location
of the point can be adjusted with the Phase Difference
slider.
- Phased Array 3: this is a group of point
sources arranged in a line, where the relative phases of each source
causes the radiation to act as if it is coming from a point source
to the left of the screen. The location
of the virtual point source can be adjusted with the Phase Difference
slider.
- Doppler Effect 1: this shows a moving source, thereby demonstrating
the Doppler effect.
- Doppler Effect 2: this shows waves being reflected by a
moving obstacle. The horizontal obstacle on the right is moving up
and down. (The divider in the middle is just there to make the
effect more clear.) When the obstacle is moving up, the reflected
waves have a higher frequency than the source. When it's moving down,
the reflections have a lower frequency.
- Sonic Boom: this shows a source moving faster than the
speed of wave propagation, creating a shock wave behind it.
- Big 1x1 Mode: this creates a small box
with a standing wave
in its normal mode of oscillation.
The inside of the box
changes color with a simple time dependence with
no left-right or up-down motion.
- 1x1 Modes: this creates several small boxes of different
sizes in their
fundamental modes. If you cut out the right side of one of the
boxes and turn up the brightness you can see waves coming out of the
box at its resonant frequency.
- 1xN Modes: this creates several small boxes in other
normal modes.
- NxN Modes: this creates several small boxes in other
normal modes.
- 1xN Mode Combos: this creates several small boxes,
each of which has a combination of two random 1xN modes.
- NxN Mode Combos: this creates several small boxes,
each of which has a combination of two random NxN modes.
- 0x1 Acoustic Modes: this creates several small boxes of
different sizes in their fundamental modes. The Fixed Edges
checkbox is off, which causes the waves to act like acoustic waves.
- 0xN Acoustic Modes: this creates several small boxes in
other acoustic normal modes. The mode frequencies are all multiples
of the fundamental, so you will see all the modes sync up periodically.
(This is not the case with the 1xN Modes example above.)
- NxN Acoustic Modes: this creates several small boxes in
other acoustic normal modes.
- Coupled Cavities: this creates pairs of boxes with a small
interconnection between them. This causes the oscillation energy
to move back and forth between the two boxes.
- Beats: this creates two sources close together with
different frequencies. Because the frequencies are close but not
exactly the same, you will see black lines of interference or "beats".
- Slow Medium: in this demonstration, the area below the blue
line has a different refractive index, so that waves move slower through
that area. As a result, waves hitting the the blue region will be partially
reflected and partially transmitted.
Waves travel through the blue region at half the speed as they
travel through the black region, so the blue region has a refractive
index of 2. As a comparison, most common types of glass have
a refractive index anywhere from 1.46 to 1.96.
- Refraction: this creates a blue region similar to the
last setup, but shows short pulses hitting it at an angle so you can
see the waves being reflected and refracted.
- Internal Reflection: this creates a blue region similar to the
last setup, but shows short pulses hitting it at an angle from inside
the blue region. The angle is such that none of the main part
of the wave is transmitted; this is called total internal reflection.
You will see some activity in the upper area; this is partly because the
top part of the wave is rounded instead of being a plane, so that
it hits the interface at a different angle (it goes up from the
source instead of diagonally). This part is transmitted, but the
plane part going diagonally is reflected. But, even for the part of
the wave that is reflected, you will a portion of the wave
travelling along the interface between the blue and black area;
but it will not propagate into the black area.
- Anti-Reflective Coating: this creates a blue region similar
to the last setup, but with an
anti-reflective
coating which eliminates
reflections. (There will be some initial reflections when the source
is first turned on because of
high-frequency components in the initial wavefront.) If you increase
the frequency of the source, you will see reflections because the
wavelength of the source no longer matches the thickness of the coating.
- Zone Plate (Even):
This creates a zone plate, which uses diffraction to focus light.
- Zone Plate (Odd):
This creates another zone plate which is similar to the previous one,
but has opaque areas made
transparent and vice versa. It also focuses light.
- Circle:
This creates a circular area with a source at the center.
Pulses will travel outward and will then be reflected back
to the center.
- Ellipse:
This creates an elliptical area with a source at one focus.
Pulses will converge at the other focus.
- Resonant Cavities 1:
This creates a series of rectangular cavities being driven by
a plane wave from above. As you change the frequency you will
see the response of each cavity change. Each cavity has a different
resonant frequency so it will respond differently. After changing
the frequency you may want to wait a bit for things to settle down
(or turn the simulation speed way up).
- Resonant Cavities 2:
This creates a series of smaller rectangular cavities.
- Room Resonance:
This shows acousting standing waves in a series of rooms being
driven by the same frequency, but at different positions. The brightness
is turned way down so you only see waves in the rooms that resonate. As
you can see, three of the rooms resonate but the fourth does not, because the
source is not located in the right place (there aren't
any modes with the right frequency that have antinodes at the source
location). By varying the frequency you can see different resonance
behavior. (You may want to turn the simulation
speed up so you get faster results as you experiment.)
- Waveguides 1:
This creates a series of waveguides of different widths.
Narrower waveguides, like at the left end of the screen,
have higher cutoff frequencies; the leftmost waveguide has a
cutoff frequency that is higher than the source, so there is no
wave motion in it. You can fix this by turning the Source
Frequency slider up.
Notice that the waves seem to be moving faster in thinner
waveguides. They appear to be moving faster than waves normally
move in the applet. This is because the phase velocity is faster in
thinner waveguides; but the signal velocity is actually slower than normal,
as you
can verify by clicking the Clear Waves button and watching the
wave move down the guide for the first time.
Since the waveguides are being driven by a plane wave, only the TE01
mode is present. (See the waveguide applet
for another way to view waveguide modes.)
- Waveguides 2:
This is just the same set of waveguides with a lower frequency, showing
that more of the guides are driven below cutoff.
- Waveguides 3:
This is a set of identical waveguides being driven by small holes at
different locations. This causes different sets of modes to be excited
in different proportions. When the guide is being driven near the center,
the TE01 mode is dominant, but when it is driven near the edge, the
TE02 mode is more prevalent. The frequency is low enough so that all
other modes are cut off. You can fix this by turning the frequency up.
By turning the frequency down, you can cut off the TE02 mode as well.
- Waveguides 4:
This is a set of acoustic waveguides being driven at various locations.
- Waveguides 5:
This is a set of identical waveguides with various modes present.
The first waveguide contains the TE01 mode; the second contains the
TE02 mode; the third contains both; the fourth contains the TE03 mode;
the fifth contains TE01 and TE03; the sixth contains TE02 and TE03.
(There may not be room on your screen for all these modes if
your resolution is not set high enough.)
Notice that the higher modes (TE02 and especially TE03) seem to be moving
faster. This is because the phase velocity of TE02 and TE03 is greater
than that of TE01.
Their signal velocities are slower, though, which is why it takes
the TE03 wave so long to make it down to the end of the waveguide.
Also if you turn off the source (by setting the source
popup to "No Sources") it will take quite a while for the TE03 mode
to stop.
- Parabolic Mirror 1:
This shows a parabola with a source at the focus. The parabola
direct the waves upward as plane waves (except at the edges where
the waves don't look planar; if we extended the parabola further
it would fix this).
- Parabolic Mirror 2:
This shows a parabola with plane waves coming from above.
They converge at the focus.
- Sound Duct:
This shows a duct with sound waves travelling through it.
When they get to the end, they are partially reflected,
even through there is nothing there for them to bounce off of.
This shows that waves are reflected by any discontinuity, not just
by walls.
- Baffled Piston:
This shows the sound radiation from a baffled piston, which is a simple model of a boxed loudspeaker.
- Low-Pass Filter 1, 2:
This shows an acoustic low-pass filter. Low-frequency waves
travel through it more easily than high-frequency waves, as you
can verify by comparing Low-Pass Filter 1 with Low-Pass
Filter 2. (These two setups are the same except for the frequency.)
However there are a few higher frequencies which will pass easily.
- High-Pass Filter 1, 2:
This shows an acoustic high-pass filter.
High-frequency waves travel through it more easily than low-frequency waves,
as you
can verify by comparing High-Pass Filter 1 with High-Pass
Filter 2.
- Band-Stop Filter 1, 2, 3:
This shows an acoustic band-stop filter, which blocks out a
range of frequencies. There are three versions of this setup; one at
a low frequency, one high, and one at the blocked frequency.
- Planar convex lens:
This shows a lens made out of a glasslike material. It focuses
plane waves. Unfortunately the lens is pretty small compared to
the wavelength of light so it won't focus the light as well as it
would in real life. This lens is only a dozen or so wavelengths
wide. The range of
visible light wavelengths is 400 to 700 nanometers, so obviously
a real lens is much larger compared to a wavelength and so will
focus better without running into diffraction effects.
- Biconvex lens:
This shows another lens. It takes line
coming from a point source and focuses it at another point.
- Planar Concave Lens:
This shows a lens that takes plane waves and spreads them out.
- Circular Prism:
This shows a round prism made out of a dense material.
- Right-Angle Prism:
This shows a prism that takes waves travelling down and points them
to the right.
- Porro Prism:
This shows a prism that takes waves travelling down and points them up.
Obviously in real life it would do this at light speed.
- Scattering:
This shows a plane wave being scattered by a point particle.
- Lloyd's Mirror:
This shows an interferometer which consists of a point source
close to a mirror (at the bottom of the window).
The waves coming from the source interfere with the waves coming
from its mirror image.
- Temperature Gradient 1:
This shows refraction of a wave due to a
temperature gradient.
The blue area represents cool air, where sound waves move more slowly.
This causes the waves to bend downwards.
- Temperature Gradient 2:
This shows refraction of a wave due to a different type of
temperature gradient.
The blue area represents cool air, where sound waves move more slowly.
This causes the waves to bend upwards.
A similar effect is responsible for mirages.
If the Mouse popup is set to Mouse = Hold Wave (+), then if you click on
a point and hold the mouse down, it will create a positive
area on the screen which will persist as long as the mouse is down.
This will cause the surrounding area to also be positive. For sound waves,
this is like adding air at that point;
it puts more pressure on the surrounding area.
The Clear Waves button clears out any waves but does not
remove any walls or sources.
The Stopped checkbox stops the applet, in case you want to
take a closer look at something, or if you want to work on something
with the mouse without worrying about it changing out from under you.
The Waves popup determines what type of waves are being simulated.
The type of waves affects two things: the screen width scale, and
the response when a wave hits a wall. For acoustic waves, waves
will be reflected with no phase change (so, positive wavefronts will
still be positive when reflected). Otherwise, waves will be reflected
negatively (positive wavefronts will be negative when reflected).
The screen width scale depends on the setting of the Waves popup, but you
can also set it manually by going to File->Options. Setting the width
of the screen in meters doesn't affect the simulation but it does
affect the coordinate display, and the values that are displayed for
object parameters (lengths, widths, wavelengths, etc).
The 3-D View checkbox gives you a 3-D view. You can rotate the
view by dragging the mouse, but you can't modify the waves or walls in
this mode. The brightness slider will adjust the height of the waves.
The Simulation Speed slider controls how far the waves move
between frames. If you slide this to the left, the applet will go
faster but the motion will be choppier.
The Resolution slider allows you to speed up or slow down the
applet by adjusting the resolution; a higher resolution is slower
but looks better.
The Brightness slider controls the brightness, just like on a
TV set. This can be used to view faint waves more easily.
Click here to go to the applet.
java@falstad.com
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero’s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ‘Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?’ ‘I have no scruples on that point,‘ replies the impatient poet. ‘But I have,’ rejoins Fuscus,—‘a little weak-minded, one of the many, you know—excuse me, another time.‘331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.’332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff’s hand was quietly coming down. “What happened to you?” begged Sandy. “Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn’t come back, I thought I’d better go and find you—and see if it meant anything to you.” She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm—foreign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do—I can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident—wud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion—fireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England—France. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently. HoME另类小说撸色
ENTER NUMBET 0017
wjl.org.cn
xunlianba.com.cn
www.tonyhawk.com.cn
www.shenglila.com.cn
cczhlj.com.cn
www.deben1.com.cn
www.linsi1.net.cn
6662016.org.cn
weiri2.net.cn
www.06vc.org.cn