This java applet is a simulation that demonstrates
scalar waves in three dimensions. Sound waves are examples of scalar
waves. (Electromagnetic waves are vector in nature, and so this applet
does not accurately simulate them.)
When the applet starts up you will see red and green waves emanating
from a source in the center of a cubic box. The wave color indicates
the acoustic pressure.
The green areas are negative and the red areas are positive.
The first thing to do when starting up the applet is to adjust the
settings for your computer. First try clicking the "Alternate Rendering"
checkbox, if it is not already checked.
Depending on your browser it may speed things up or slow things
down. If it makes things slower then uncheck it.
Next, slide the "Image Resolution" slider to the right as far as you can
without slowing things down too much. Or you could slide it to the left
if things are already too slow.
Another thing to try, if the simulation is too
slow, is to slide the "Simulation Speed" button to the right. That won't
improve the framerate but it
will get the waves moving faster.
The Setup popup can be used to select one of the following
experiments:
- Point Source: this is a single point source emitting
spherical waves.
- Pinhole: this is also just a point source, but it is off to one
side.
- 2 Point Sources: here we have two point sources, creating an
interference pattern, which becomes much more apparent if you raise the
frequency. The "Source Separation" slider can be used to
adjust the distance between the two sources. The "Phase Difference"
can be used to adjust the relative phase of their waves.
The "Balance" slider is like the balance dial on a radio; if you put it
in the middle, both sources are equally strong, but if you put it off
to one side, then one source becomes stronger at the expense of the other.
- Dipole Source: this demonstrates a dipole source consisting of
two sources out of phase.
- Lateral Quadrupole: this demonstrates a quadrupole
source consisting of
four sources arranged in a square.
- Linear Quadrupole: this demonstrates a quadrupole
source consisting of
four sources arranged in a line.
- 2 Pinholes: This is just two point sources off to one side.
- Single Line Source: this is a single line source emitting
cylindrical waves.
- Single Slit: this is a line source off to one side.
- 2 Line Sources: this is two line sources interfering.
You can adjust the separation, the phase difference, and the balance,
as above with 2 point sources.
- Double Slit: this is two line sources interfering,
but they are off to one side.
- Triple Slit: this is three line sources interfering.
- Plane Wave: planar wavefronts travelling in one direction.
- 2 Plane Waves: this is two overlapping plane waves.
You can control the direction of the first plane wave by setting
theta and phi; these are just the angles of the propagation direction
in spherical coordinates. Also the balance can be adjusted.
If you set the balance slider all the way to the left, then only
the first plane wave is present, so you can more easily get the feel for how
the theta and phi sliders affect the direction of the wave.
The Stopped checkbox will stop and start the applet.
The Show Intensity checkbox will show the intensity of the
wave rather than the acoustic pressure.
The Show Sides checkbox will show the acoustic pressure
(or intensity) only at the edges of the box rather than inside it.
The Mouse popup controls what happens when the mouse is
clicked and dragged. If the popup is set to Mouse = Adjust Angle,
then the mouse controls the orientation of the box. If it is set
to Mouse = Adjust Zoom, you will be able to zoom in or zoom out
by dragging the mouse to the left or right.
The Slice popup allows you to look at planar slices of the box
rather than looking at the contents of the entire box.
If the popup is set to No Slicing, you view the entire
box. Otherwise you will see the box sliced in one of three
directions. The location of the slice can be adjusted by dragging
the line running along the sides of box near the slice.
The Simulation Speed slider will speed up or slow down the
oscillation.
The Brightness slider controls the brightness, just like on a
TV set. This can be used to view faint waves more easily.
The Image Resolution slider controls the resolution of the
box image. Higher resolution images are slower.
The Frequency slider controls the frequency of the wave.
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.