Click here to go to the applet.
This java applet is a simulation that demonstrates wave motion
in a perfectly elastic circular membrane (like a drum head).
An ideal continuous membrane has an infinite number of vibrational modes,
each with its own frequency. The lowest-frequency mode is called the
fundamental, and involves the entire membrane vibrating up and down
at a frequency determined by the membrane's size, tension, and mass.
The other modes involve parts of the
membrane (called nodal lines) standing still while the rest of the membrane
vibrates. When a membrane is vibrating, more than one mode is typically
present at once.
At the top of the applet on the left you will see the membrane.
To set it in motion, click Fundamental.
If you click Clear, it will be at rest again.
Below the membrane you will see a graph showing each
normal mode's contribution to the membrane's vibration.
The modes are laid out in the following order:
| 0,1 |
1,1a |
1,1b |
2,1a |
2,1b |
... |
| 0,2 |
1,2a |
1,2b |
2,2a |
2,2b |
... |
| ... |
... |
... |
... |
... |
... |
where m,n refers to the mode with m nodal diameters
and n nodal circles. Each mode with nonzero m is
doubly degenerate; the difference between the two modes is a rotation.
By combining the two degenerate modes in different proportions
you can rotate the mode arbitrarily; by combining the two modes
with different phases you can get the nodal diameters to rotate
with time.
Each element of the grid has a color which indicates the presence or
absence of the mode it represents. Black means the mode is not present;
green means the mode is present with a positive coefficient, and red means
it is present with a negative coefficient.
In addition, each mode may have a phase shift, which indicates that its
oscillatory cycle leads or lags the others. This is indicated by
a blue line.
You can add or remove a mode by clicking on it. If you click and drag
up and down you can fine-tune the magnitude of the mode. If you drag
left and right you can alter the phase shift.
The Mouse popup controls what happens when you click on the
membrane. If you set it to Poke membrane, the membrane will
be poked at the point where you click, affecting the entire
membrane. If you set the popup to Strike membrane, the membrane will
be struck at the point where you click, affecting only a small area
surrounding that point.
If you set it to Adjust view angle or Adjust view zoom, you can
adjust the orientation or size of the 3-d view.
The Display popup can be used to control whether the 3-d or 2-d
view is shown. By default it is set to Display 3-d Only. To show a
2-d representation, you can select Display 2d Only or Display 3d+2d.
The 2-d representation often gives you a clearer picture of what is
going on.
The 3d View popup can be used to control the look of the 3-d view.
By default it is set to Solid, but you can also see a wireframe
view by selecting one of the other options.
The Stopped checkbox can be used to stop the motion of the membrane
for a moment.
The Show Frequencies checkbox can be used to show or hide
the frequency grid. By default, it is shown.
The Color checkbox can be used to turn off color. This may
look better and/or it may make the applet run faster.
The Sound checkbox allows you to hear the sound the membrane
would make. High frequencies (above 4000Hz) will not be heard. This
checkbox is only present if you have Java 2 installed.
The Simulation Speed slider controls how fast the simulation will
proceed.
The Damping slider controls how much damping there is. Damping is
a force that slows the membrane down. High harmonics are damped more than lower ones.
The default
setting is set to zero, so you may want to set this higher in order to
get more realistic behavior.
The Brightness slider controls the brightness, just like on a
TV set. This can be used to view faint waves more easily.
The Resolution slider will adjust the fineness of the
rendering. This can be set lower to speed up the applet.
The Base Frequency slider will adjust the fundamental frequency of the
membrane, when the Sound checkbox is on. Normally this would be
determined by the tension, size, and mass of the membrane.
Back 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.