Wavelength and amplitude. Are they related? | Physics Forums
Nov 16, This is true for light waves, 26 oct relation between frequency and wavelength of. Wave parameters wavelength, amplitude, period. Aug 19, If higher the amplitude the particles move a larger distance right. So is the wavelength related to amplitude. Of course we don't trust wikipedia: . linear differential equation) at large amplitudes because the displacement of. Cartoon representation of a standing wave with nodes and antinodes identified Compared to traveling waves with the same amplitude, producing standing waves is It should become obvious that we will get the same relationships for the . Well I don't want to prove that right now so you'll have to trust me, but there are.
- Wave Parameters
Often they are also connected to a satellite communication system. Such systems enable us to receive seismic signals from all over the world, soon after an earthquake.
Standing Waves – The Physics Hypertextbook
A real-time seismic recording system with digital storage and satellite communications. Ground vibrations are detected by the sensor, digitally recorded, and then transmitted via satellite. Classic Seismograms For most of the last century, seismograms were recorded on sheet of paper, either with ink or photographically.
We call such records "analog" records to distinguish them from digital recordings. These records are read just like a book - from top-to-bottom and left-to-right. The classic paper seismogram is read like a book, from left-to-right and top to bottom. A continuous record is constructed by drawing the line as a sheet of paper fastened to a rotating drum constantly moves horizontally on a threaded attachment.
When the ground vibrates the pen moves up or down creating th seismic record of the vibrations. Seismograph station and component, date and start time are recorded on the upper left of this paper.
One problem with these mechanical systems was the limited range of ground motion that could be recorded - vibrations smaller than a line thickness and those beyond the physical range of the ink pen were lost.
To circumvent these limitations we often operated high and low-gain instruments side-by-side, but that was neither as efficient nor effective as the modern digital electronic instruments. However, modern "digital" or computerized instruments are relatively new, only about years old, and most of our data regarding large earthquakes are actually recorded on paper or film.
Additionally, we still use paper recording systems for display purposes so we can see what is going on without a computer. Digital Seismograms Today, most seismic data are recorded digitally, which facilitates quick interpretations of the signals using computers.
Digital seismograms are "sampled" at an even time interval that depends on the type of seismic instrument and the interest of the people who deploy the seismometer. The same principle is used to provide "digital" sound on compact disks. The motion of the ground is continuous, but we can pick only certain positions and reconstruct the motion within certain limits. A digital seismogram is a record of the ground movement stored as an array of numbers which indicate the time and the movement of the ground for a range of times and are easily analyzed using computers.
The principle is the same as that used for digital audio signals that are stored on Music CD's. Also, since with live in a three-dimensional space, to record the complete ground motion, we must record the motion in three directions. Usually, we usually choose: Up-down North-south East-west With three records of ground motion in three directions, a single seismic station that records about 20 samples per second must store or transmit about 3 x 1.
Seismometers Before technological advances in the last few decades, to record seismic signals we developed and deployed many different kinds of seismometers.
In the 's, as part of an effort to verify underground nuclear test threshold treaties, two seismometer models became standard for global earthquake analyses, the world-wide network long-period and short-period instruments. These instruments have been replaced by "broad-band" instruments which can detect ground motions over large ranges, or "bands", of periods. However, since much of our historical data are recorded on the older "narrow-band" short-period and long-period instruments, they remain important sources of data.
Different seismometers record different frequencies or periods of ground motion and are analogous to different colors in a picture. Seismometer Response Curves Seismometers are usually designed to record signals over a specified range of frequencies or periods so it is convenient to discuss instruments based on the range of vibration frequencies that they can detect.
Thus one way to characterize seismometers is to describe the range of vibration frequencies that they can detect. A plot of the amplification as a versus frequency is called an instrument response. An instrument is sensitive to vibrations at frequencies for which the "response" curve is relatively large. Five sample instrument response curves are shown below.
The vertical axis shows the ground-motion amplification factor. To characterize an instrument, what's really important is the range of amplitudes, not the specific amplification, which is usually adjusted depending on the location of the seismometer. I have used numbers around one to illustrate the differences between the response curves for different instruments but actual amplification factors are usually much larger than those shown.
The yellow region is the low end of the frequency range audible to most humans we can hear waves around 20 hertz to 20, hertz. The same broad-band response is shown in the right panel, to compare the response with a special short-period instrument, the Wood-Anderson, and an accelerometer.
The Wood-Anderson short-period instrument was the one that Charles Richter used to develop his magnitude scale for southern California. The accelerometer is an instrument designed to record large amplitude and high-frequency shaking near large earthquakes.
Those are the vibrations that are important in building, highway, etc. Seismograms The figure below shows the results of different recording instruments on the measurements of ground motion displacement for an earthquake that occurred in Texas, in The observations were recorded on a broad-band instrument and the signals that would have been recorded on the WWSSN instrument types were simulated using a little mathematics since all the vibrations that would be detected by the long- and short-period seismometers are also recorded by the broadband seismometer.
The above diagram shows the ground displacement observed near Tucson, Arizona, caused by an earthquake in southwestern Texas. The top panel shows the vibrations measured using a broad-band seismometer, the middle panel shows the vibrations as they would be detected by the long-period sensor, and the bottom panel the vibrations that would be sensed by a short-period sensor scaled by a factor of 10 so we can see them better. Accelerometers Another important class of seismometers was developed for recording large amplitude vibrations that are common within a few tens of kilometers of large earthquakes - these are called strong-motion seismometers.
Strong-motion instruments were designed to record the high accelerations that are particularly important for designing buildings and other structures. Traveling waves have high points called crests and low points called troughs in the transverse case or compressed points called compressions and stretched points called rarefactions in the longitudinal case that travel through the medium.
Standing waves don't go anywhere, but they do have regions where the disturbance of the wave is quite small, almost zero. These locations are called nodes. There are also regions where the disturbance is quite intense, greater than anywhere else in the medium, called antinodes.
Standing waves can form under a variety of conditions, but they are easily demonstrated in a medium which is finite or bounded. A phone cord begins at the base and ends at the handset. Or is it the other way around? Other simple examples of finite media are a guitar string it runs from fret to bridgea drum head it's bounded by the rimthe air in a room it's bounded by the wallsthe water in Lake Michigan it's bounded by the shoresor the surface of the Earth although not bounded, the surface of the Earth is finite.
In general, standing waves can be produced by any two identical waves traveling in opposite directions that have the right wavelength.
In a bounded medium, standing waves occur when a wave with the correct wavelength meets its reflection. The interference of these two waves produces a resultant wave that does not appear to move. Standing waves don't form under just any circumstances. They require that energy be fed into a system at an appropriate frequency. This condition is known as resonance.
Wavelength and amplitude. Are they related?
Standing waves are always associated with resonance. Resonance can be identified by a dramatic increase in amplitude of the resultant vibrations. Compared to traveling waves with the same amplitude, producing standing waves is relatively effortless. In the case of the telephone cord, small motions in the hand result will result in much larger motions of the telephone cord.
Velocity, Amplitude, Wavelength, And Frequency - The Measures Of A Wave
Any system in which standing waves can form has numerous natural frequencies. The set of all possible standing waves are known as the harmonics of a system.
The harmonics above the fundamental, especially in music theory, are sometimes also called overtones. What wavelengths will form standing waves in a simple, one-dimensional system? There are three simple cases. The simplest standing wave that can form under these circumstances has one antinode in the middle. This is half a wavelength. To make the next possible standing wave, place a node in the center. We now have one whole wavelength. To make the third possible standing wave, divide the length into thirds by adding another node.
This gives us one and a half wavelengths. It should become obvious that to continue all that is needed is to keep adding nodes, dividing the medium into fourths, then fifths, sixths, etc. There are important relations among the harmonics themselves in this sequence.
Since frequency is inversely proportional to wavelength, the frequencies are also related. The simplest standing wave that can form under these circumstances has one node in the middle. To make the next possible standing wave, place another antinode in the center.
To make the third possible standing wave, divide the length into thirds by adding another antinode. It should become obvious that we will get the same relationships for the standing waves formed between two free ends that we have for two fixed ends. The only difference is that the nodes have been replaced with antinodes and vice versa. Thus when standing waves form in a linear medium that has two free ends a whole number of half wavelengths fit inside the medium and the overtones are whole number multiples of the fundamental frequency one dimension: A node will always form at the fixed end while an antinode will always form at the free end.
The simplest standing wave that can form under these circumstances is one-quarter wavelength long. To make the next possible standing wave add both a node and an antinode, dividing the drawing up into thirds.
We now have three-quarters of a wavelength. Repeating this procedure we get five-quarters of a wavelength, then seven-quarters, etc. In this arrangement, there are always an odd number of quarter wavelengths present. Thus the wavelengths of the harmonics are always fractional multiples of the fundamental wavelength with an odd number in the denominator. Likewise, the frequencies of the harmonics are always odd multiples of the fundamental frequency.
The three cases above show that, although not all frequencies will result in standing waves, a simple, one-dimensional system possesses an infinite number of natural frequencies that will.
Wave Parameters: Wavelength, Amplitude, Period, Frequency & Speed
It also shows that these frequencies are simple multiples of some fundamental frequency. For any real-world system, however, the higher frequency standing waves are difficult if not impossible to produce. Tuning forks, for example, vibrate strongly at the fundamental frequency, very little at the second harmonic, and effectively not at all at the higher harmonics.
It seems like getting something for nothing. Put a little bit of energy in at the right rate and watch it accumulate into something with a lot of energy.