What is the correct specific gravity. Specific gravity

WHAT IS RADIO WAVES

Radio waves are electromagnetic oscillations propagating in space at the speed of light (300,000 km/sec). By the way, light is also electromagnetic waves that have properties similar to radio waves (reflection, refraction, attenuation, etc.).

Radio waves carry through space the energy emitted by the generator of electromagnetic oscillations. And they are born when the electric field changes, for example, when an alternating electric current passes through the conductor or when sparks jump through space, i.e. a series of fast successive current pulses.

Electromagnetic radiation is characterized by frequency, wavelength and the power of the transferred energy. The frequency of electromagnetic waves shows how many times per second the direction of the electric current changes in the emitter and, therefore, how many times per second the magnitude of the electric and magnetic fields changes at each point in space. The frequency is measured in hertz (Hz) - units named after the great German scientist Heinrich Rudolf Hertz. 1 Hz is one oscillation per second, 1 megahertz (MHz) is one million oscillations per second. Knowing that the speed of electromagnetic waves is equal to the speed of light, it is possible to determine the distance between points in space where the electric (or magnetic) field is in the same phase. This distance is called the wavelength. The wavelength in meters is calculated by the formula:

Or approximately
where f is the frequency of electromagnetic radiation in MHz.

The formula shows that, for example, a frequency of 1 MHz corresponds to a wavelength of approx. 300 m. With increasing frequency, the wavelength decreases, with a decrease - guess for yourself. In the future, we will see that the wavelength directly affects the length of the antenna for radio communication.

Electromagnetic waves freely pass through air or outer space (vacuum). But if a metal wire, an antenna or any other conductive body is encountered in the path of the waves, then they give it their energy, thereby causing an alternating electric current in this conductor. But not all of the wave energy is absorbed by the conductor, part of it is reflected from its surface and either goes back or is scattered in space. By the way, the use of electromagnetic waves in radar is based on this.

Another useful property of electromagnetic waves is their ability to go around some obstacles in their path. But this is only possible if the dimensions of the object are smaller than the wavelength, or comparable to it. For example, in order to detect an aircraft, the length of the radio wave of the locator must be less than its geometric dimensions (less than 10 m). If the body is longer than the wavelength, it can reflect it. But it may not reflect. Recall the military stealth technology "Stealth", which developed the appropriate geometric shapes, radar-absorbing materials and coatings to reduce the visibility of objects for radars.

The energy carried by electromagnetic waves depends on the power of the generator (emitter) and the distance to it. Scientifically, it sounds like this: the energy flux per unit area is directly proportional to the radiation power and inversely proportional to the square of the distance to the emitter. This means that the communication range depends on the power of the transmitter, but to a much greater extent on the distance to it.

SPECTRUM DISTRIBUTION

Radio waves used in radio engineering occupy an area, or more scientifically - a spectrum from 10,000 m (30 kHz) to 0.1 mm (3,000 GHz). This is only part of the vast spectrum of electromagnetic waves. Radio waves (in descending length) are followed by thermal or infrared rays. After them comes a narrow section of visible light waves, then a spectrum of ultraviolet, x-ray and gamma rays - all these are electromagnetic oscillations of the same nature, differing only in wavelength and, therefore, in frequency.

Although the entire spectrum is divided into regions, the boundaries between them are outlined conditionally. Regions follow continuously one after another, pass one into another, and in some cases overlap.

By international agreements, the entire spectrum of radio waves used in radio communications is divided into ranges:

Range frequencies	Frequency band name	Name wave range	Wavelength
	Very low frequencies (VLF)	Myriameter
	Low frequencies (LF)	Kilometer
300-3000 kHz	Middle frequencies (MF)	Hectometric
	Treble (HF)	Decameter
	Very high frequencies (VHF)	Meter
300-3000 MHz	Ultra high frequencies (UHF)	decimeter
	Ultra high frequencies (SHF)	centimeter
	Extreme high frequencies (EHF)	Millimeter
300-3000 GHz	Hyper high frequencies (HHF)	decimillimeter

But these ranges are very extensive and, in turn, are divided into sections, which include the so-called broadcasting and television ranges, ranges for land and aviation, space and maritime communications, for data transmission and medicine, for radar and radio navigation, etc. Each radio service has its own section of the range or fixed frequencies.

Spectrum allocation between different services.

This breakdown is quite confusing, which is why many services use their own "internal" terminology. Usually, the following names are used when designating the ranges allocated for land mobile communications:

	Frequency range	Explanations
		Due to the nature of propagation, it is mainly used for long-distance communications.
	25.6–30.1 MHz	Civil band in which private individuals can use communications. In different countries, from 40 to 80 fixed frequencies (channels) are allocated in this section.
		Range of mobile terrestrial communication. It is not clear why, but in Russian there was no term that defines this range.
	136-174 MHz	Most common terrestrial mobile band.
	400-512 MHz	Range of mobile terrestrial communication. Sometimes this section is not singled out as a separate range, but they say VHF, meaning the frequency band from 136 to 512 MHz.
	806–825 and 851–870 MHz	Traditional "American" range; widely used by mobile communications in the United States. We have not received much distribution.

Do not confuse the official names of frequency bands with the names of sections allocated to various services. It should be noted that the world's major manufacturers of equipment for mobile terrestrial communications produce models designed to work within these areas.

In the following, we will talk about the properties of radio waves in relation to their use in terrestrial mobile radio communications.

HOW RADIO WAVES PROPAGATE

Radio waves are radiated through an antenna into space and propagate in the form of electromagnetic field energy. And although the nature of radio waves is the same, their ability to propagate strongly depends on the wavelength.

Ground for radio waves is a conductor of electricity (although not a very good one). Passing over the surface of the earth, radio waves gradually weaken. This is due to the fact that electromagnetic waves excite electric currents in the surface of the earth, for which part of the energy is spent. Those. the energy is absorbed by the earth, and the more, the shorter the wavelength (the higher the frequency).

In addition, the wave energy weakens also because the radiation propagates in all directions of space and, therefore, the farther the receiver is from the transmitter, the less energy per unit area and the less it enters the antenna.

Transmissions of long-wave broadcast stations can be received at distances of up to several thousand kilometers, and the signal level decreases smoothly, without jumps. Medium wave stations are audible within a thousand kilometers. As for short waves, their energy decreases sharply with distance from the transmitter. This explains the fact that at the dawn of the development of radio, waves from 1 to 30 km were mainly used for communication. Waves shorter than 100 meters were generally considered unsuitable for long-distance communications.

However, further studies of short and ultrashort waves showed that they quickly decay when they travel near the Earth's surface. When the radiation is directed upwards, short waves come back.

Back in 1902, English mathematician Oliver Heaviside and American electrical engineer Arthur Edwin Kennelly almost simultaneously predicted that an ionized layer of air exists above the Earth - a natural mirror that reflects electromagnetic waves. This layer was called the ionosphere.

The Earth's ionosphere was supposed to make it possible to increase the range of propagation of radio waves to distances exceeding the line of sight. Experimentally, this assumption was proved in 1923. Radio frequency pulses were transmitted vertically upwards and returned signals were received. Measurements of the time between sending and receiving pulses made it possible to determine the height and number of reflection layers.

Propagation of long and short waves.

Reflected from the ionosphere, short waves return to the Earth, leaving hundreds of kilometers of the "dead zone" under them. Having traveled to the ionosphere and back, the wave does not “calm down”, but is reflected from the surface of the Earth and again rushes to the ionosphere, where it is reflected again, etc. Thus, repeatedly reflected, the radio wave can go around the globe several times.

It was found that the reflection height depends primarily on the wavelength. The shorter the wave, the higher its reflection occurs and, consequently, the larger the “dead zone”. This dependence is true only for the short-wavelength part of the spectrum (up to approximately 25–30 MHz). For shorter wavelengths, the ionosphere is transparent. Waves penetrate it through and through and go into outer space.

It can be seen from the figure that the reflection depends not only on the frequency, but also on the time of day. This is due to the fact that the ionosphere is ionized by solar radiation and gradually loses its reflectivity with the onset of darkness. The degree of ionization also depends on solar activity, which varies throughout the year and from year to year in a seven-year cycle.

Reflective layers of the ionosphere and the propagation of short waves depending on the frequency and time of day.

Radio waves in the VHF range are more similar in properties to light rays. They practically do not reflect from the ionosphere, very slightly bend around the earth's surface and propagate within the line of sight. Therefore, the range of action of ultrashort waves is small. But this has a certain advantage for radio communications. Since the waves propagate within the line of sight in the VHF range, radio stations can be located at a distance of 150–200 km from each other without mutual influence. And this allows you to repeatedly use the same frequency to neighboring stations.

Propagation of short and ultrashort waves.

The properties of radio waves in the ranges of DTSV and 800 MHz are even closer to light rays and therefore have another interesting and important property. Let's remember how a flashlight is arranged. Light from a bulb located at the focus of the reflector is collected in a narrow beam of rays that can be sent in any direction. Approximately the same can be done with high-frequency radio waves. You can collect them with antenna mirrors and send them in narrow beams. It is impossible to build such an antenna for low-frequency waves, since its dimensions would be too large (the diameter of the mirror must be much larger than the wavelength).

The possibility of directed emission of waves makes it possible to increase the efficiency of the communication system. This is due to the fact that a narrow beam provides less energy dissipation in side directions, which allows the use of less powerful transmitters to achieve a given communication range. Directional radiation creates less interference with other communication systems that are not in the beam site.

When receiving radio waves, the advantages of directional radiation can also be used. For example, many people are familiar with parabolic satellite dishes, which focus the radiation of a satellite transmitter to the point where the receiving sensor is installed. The use of directional receiving antennas in radio astronomy has made it possible to make many fundamental scientific discoveries. The ability to focus high-frequency radio waves has ensured their wide application in radar, radio relay communications, satellite broadcasting, wireless data transmission, etc.

Parabolic directional satellite dish (photo from ru.wikipedia.org).

It should be noted that with decreasing wavelength, the attenuation and absorption of energy in the atmosphere increase. In particular, the propagation of waves shorter than 1 cm begins to be affected by such phenomena as fog, rain, clouds, which can become a serious obstacle that limits the communication range.

We have found that radio waves have different propagation properties depending on the wavelength, and each section of the radio spectrum is used where its advantages are best used.

>>Physics: Velocity and wavelength

Each wave propagates at a certain speed. Under wave speed understand the propagation speed of the disturbance. For example, a blow to the end of a steel rod causes local compression in it, which then propagates along the rod at a speed of about 5 km/s.

The speed of a wave is determined by the properties of the medium in which this wave propagates. When a wave passes from one medium to another, its speed changes.

In addition to speed, an important characteristic of a wave is its wavelength. Wavelength called the distance over which a wave propagates in a time equal to the period of oscillations in it.

The direction of the spread of the war

Since the speed of the wave is a constant value (for a given medium), the distance traveled by the wave is equal to the product of the speed and the time of its propagation. Thus, to find the wavelength, you need to multiply the speed of the wave by the period of oscillation in it:

By choosing the direction of wave propagation for the direction of the x axis and denoting by y the coordinate of the particles oscillating in the wave, we can construct wave chart. A sine wave graph (for a fixed time t) is shown in Figure 45.

The distance between adjacent crests (or troughs) on this graph is the same as the wavelength.

Formula (22.1) expresses the relationship of the wavelength with its speed and period. Considering that the period of oscillations in a wave is inversely proportional to the frequency, i.e. T=1/ v, you can get a formula expressing the relationship of the wavelength with its speed and frequency:

The resulting formula shows that the speed of a wave is equal to the product of the wavelength and the frequency of oscillations in it.

The frequency of oscillations in the wave coincides with the frequency of oscillations of the source (since the oscillations of the particles of the medium are forced) and does not depend on the properties of the medium in which the wave propagates. When a wave passes from one medium to another, its frequency does not change, only the speed and wavelength change.

??? 1. What is meant by wave speed? 2. What is the wavelength? 3. How is the wavelength related to the speed and period of oscillations in a wave? 4. How is the wavelength related to the speed and frequency of oscillations in a wave? 5. Which of the following wave characteristics change when a wave passes from one medium to another: a) frequency; b) period; c) speed; d) wavelength?

Experimental task . Pour water into the tub and, by rhythmically touching the water with your finger (or a ruler), create waves on its surface. Using different oscillation frequencies (for example, touching the water once and twice per second), pay attention to the distance between adjacent wave crests. At what frequency is the wavelength longer?

S.V. Gromov, N.A. Motherland, Physics Grade 8

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The wavelength can also be determined:

as the distance, measured in the direction of wave propagation, between two points in space at which the phase of the oscillatory process differs by 2π;
as the path that the wave front passes over a time interval equal to the period of the oscillatory process;
as spatial period wave process.

Let us imagine the waves arising in the water from a uniformly oscillating float, and mentally stop time. Then the wavelength is the distance between two adjacent wave crests, measured in the radial direction. Wavelength is one of the main characteristics of a wave, along with frequency, amplitude, initial phase, propagation direction, and polarization. The Greek letter is used to denote the wavelength λ (\displaystyle \lambda ), the dimension of the wavelength is a meter.

As a rule, the wavelength is used in relation to a harmonic or quasi-harmonic (for example, damped or narrow-band modulated) wave process in a homogeneous, quasi-homogeneous or locally homogeneous medium. However, formally, the wavelength can be determined by analogy for a wave process with a non-harmonic, but periodic space-time dependence, containing a set of harmonics in the spectrum. Then the wavelength will coincide with the wavelength of the fundamental (lowest-frequency, fundamental) harmonic of the spectrum.

Encyclopedic YouTube

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Amplitude, period, frequency and wavelength of periodic waves

Sound vibrations - Wavelength

5.7 Wavelength. Wave speed

Lesson 370 Velocity of a transverse wave in a string

Lesson 369 Mathematical description of a traveling wave

Subtitles

In the last video, we discussed what happens if you take, say, a rope, pull the left end - this, of course, can be the right end, but let it be the left - so, pull up, and then down and then back to the original position. We convey some kind of indignation to the rope. This perturbation might look something like this if I pull the rope up and down once. The perturbation will be transmitted along the rope approximately in this way. Let's paint it black. Right after the first cycle - jerking up and down - the rope will look something like this. But if you wait a bit, it will look something like this, given that we pulled once. The impulse is transmitted further along the rope. In the last video, we defined this perturbation to be transmitted along the rope or in a given medium, although the medium is not a necessary condition. We called it the wave. And, in particular, this wave is an impulse. This is an impulsive wave, because there was essentially only one perturbation of the rope. But if we continue to periodically pull the rope up and down at regular intervals, then it will look something like this. I'll try to be as accurate as possible. It will look like this, and vibrations, or perturbations, will be transmitted to the right. They will be transmitted to the right at a certain speed. And in this video I want to consider exactly this type of waves. Imagine that I periodically pull the left end of the rope up and down, up and down, creating periodic oscillations. We will call it periodic waves. This is a periodic wave. The movement is repeated over and over. Now I would like to discuss some properties of a periodic wave. First, you can see that as it moves, the rope goes up and down some distance from its original position, that's it. How far are the highest and lowest points from the starting position? This is called the amplitude of the wave. This distance (I'll highlight it in magenta) - this distance is called amplitude. Sailors sometimes talk about the height of the wave. Height usually refers to the distance from the base of the wave to its crest. We are talking about the amplitude, or the distance from the initial, equilibrium position to the maximum. Let's define the maximum. This is the highest point. The highest point of a wave, or its top. And this is the sole. If you were sitting in a boat, you would be interested in the height of the wave, the entire distance from your boat to the highest point of the wave. Okay, let's not get off topic. That's what's interesting. Not all waves are created by me pulling the left end of the rope. But I think you understand that this circuit can show many different types of waves. And this is essentially a deviation from the average, or zero, position, amplitude. The question arises. It's clear how far the rope deviates from the middle position, but how often does this happen? How long does it take for the rope to rise, fall, and return? How long does each cycle last? A cycle is a movement up, down and back to the starting point. How long is each cycle? Can you tell how long each period is? We said that it is a periodic wave. A period is a repetition of a wave. The duration of one complete cycle is called a period. And a period is measured by time. Maybe I pull the rope every two seconds. It takes two seconds for it to rise, fall, and return to the middle. The period is two seconds. And another close characteristic - how many cycles per second do I do? In other words, how many seconds are there in each cycle? Let's write it down. How many cycles per second do I generate? That is, how many seconds are there in each cycle? How many seconds are there for each cycle? So the period, for example, can be 5 seconds per cycle. Or maybe 2 seconds. But how many cycles occur per second? Let's ask the opposite question. It takes a few seconds to go up, down and back to the middle. And how many cycles of descent, ascent and return fit in every second? How many cycles occur per second? This property is the opposite of a period. The period is usually denoted by a capital T. This is the frequency. Let's write down. Frequency. It is usually denoted with a lowercase f. It characterizes the number of oscillations per second. So if a full cycle takes 5 seconds, this means that we will have 1/5 of a cycle happening per second. I just reversed this ratio. This is quite logical. Because period and frequency are opposite characteristics of each other. This is how many seconds in a cycle? How long does it take to get up, down and back? And this is how many descents, ascents and returns in one second? So they are inverse to each other. We can say that the frequency is equal to the ratio of unity to the period. Or the period is equal to the ratio of one to the frequency. So if the rope vibrates at a rate of, say, 10 cycles per second... And by the way, the unit of frequency is hertz, so let's write it down as 10 hertz. You've probably heard something similar before. 10 Hz simply means 10 cycles per second. If the frequency is 10 cycles per second, then the period is its ratio to one. We divide 1 by 10 seconds, which is quite logical. If a rope can rise, fall, and return to its neutral position 10 times per second, then it will do so once in 1/10 of a second. We are also interested in how fast the wave propagates in this case to the right? If I pull on the left end of the rope, how fast does it move to the right? This is speed. To find out, we need to calculate how far the wave travels in one cycle. Or for one period. After I tug once, how far will the wave go? What is the distance from this point at the neutral level to this point? This is called the wavelength. Wavelength. It can be defined in many ways. We can say that the wavelength is the distance that the initial pulse travels in one cycle. Or that it is the distance from one highest point to another. This is also the wavelength. Or the distance from one sole to another sole. This is also the wavelength. But in general, the wavelength is the distance between two identical points on the wave. From this point to this. This is also the wavelength. This is the distance between the beginning of one complete cycle and its completion at exactly the same point. At the same time, when I talk about the same points, this point is not considered. Because at a given point, although it is in the same position, the wave descends. And we need a point where the wave is in the same phase. Look, there's an upward movement going on here. So we need a lift phase. This distance is not the wavelength. To walk one length, you need to go into the same phase. It needs to move in the same direction. This is also the wavelength. So, if we know how far the wave travels in one period ... Let's write it down: the wavelength is equal to the distance that the wave travels in one period. The wavelength is equal to the distance that the wave travels in one period. Or, one might say, in one cycle. This is the same. Because the period is the time for which the wave completes one cycle. One ascent, descent and return to the zero point. So if we know the distance and time it takes a wave to travel, that is, the period, how can we calculate the speed? The speed is equal to the ratio of the distance to the time of movement. Speed is the ratio of distance to time of movement. And for a wave, the speed could be designated as a vector, but this, I think, is already clear. So, speed reflects how far a wave travels in a period? And the distance itself is the wavelength. The wave impulse will travel exactly that much. This will be the wavelength. So we walk this distance, and how long does it take? This distance is covered in a period. That is, it is the wavelength divided by the period. The wavelength divided by the period. But we already know that the ratio of unit to period is the same as frequency. So you can write it as a wavelength ... And, by the way, an important point. Wavelength is usually denoted by the Greek letter lambda. So, we can say that the speed is equal to the wavelength divided by the period. Which is equal to the wavelength multiplied by one divided by the period. We just found out that the ratio of unit to period is the same as frequency. So the speed is equal to the product of the wavelength and the frequency. Thus, you will solve all the main problems that you may encounter in the topic of waves. For example, if we are given that the speed is 100 meters per second and is directed to the right ... Let's make such an assumption. Velocity is a vector, and you need to specify its direction. Let the frequency be, say, 20 cycles per second, which is the same as 20 Hz. So, once again, the frequency will be 20 cycles per second, or 20 Hz. Imagine that you are looking through a small window and you see only this part of the wave, only this part of my rope. If you know about 20 Hz, then you know that in 1 second you will see 20 descents and ascents. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13... In 1 second, you will see the wave rise and fall 20 times. That's what a frequency of 20 Hz means, or 20 cycles per second. So, we are given speed, given frequency. What will be the wavelength? In this case, it will be equal to ... Let's go back to speed: speed is equal to the product of wavelength and frequency, right? Let's divide both parts by 20. By the way, let's check the units of measure: it's meters per second. It turns out: λ times 20 cycles per second. λ times 20 cycles per second. If we divide both parts by 20 cycles per second, we get 100 meters per second times 1/20 of a second per cycle. Here remains 5. Here 1. We get 5, the seconds are reduced. And we get 5 meters per cycle. 5 meters per cycle in this case will be the wavelength. 5 meters per cycle. Amazing. One could say that this is 5 meters per cycle, but the wavelength suggests that it means the distance traveled per cycle. In this case, if the wave propagates to the right at a speed of 100 meters per second, and this is the frequency (we see that the wave oscillates up and down 20 times per second), then this distance should be 5 meters. The period can be calculated in the same way. The period is equal to the ratio of unity to the frequency. It is equal to 1/20 of a second per cycle. 1/20 second per cycle. I don't want you to memorize formulas, I want you to understand their logic. I hope this video helped you. Using formulas, you can answer almost any question as long as there are 2 variables and a third needs to be calculated. I hope this will be useful for you. Subtitles by the Amara.org community

Wavelength - spatial period of the wave process

Wavelength in the medium

In an optically denser medium (the layer is highlighted in dark), the length of the electromagnetic wave is reduced. The blue line is the distribution of the instantaneous ( t= const) values of the wave field strength along the direction of propagation. The change in the amplitude of the field strength, due to reflection from the interfaces and the interference of the incident and reflected waves, is conventionally not shown in the figure.

Light plays an important role in photography. The usual sunlight has a rather complex spectral composition.

The spectral composition of the visible part of sunlight is characterized by the presence of monochromatic radiation, the wavelength of which is in the range of 400-720 nm, according to other sources, 380-780 nm.

In other words, sunlight can be decomposed into monochromatic components. At the same time, the monochromatic (or single color) components of daylight cannot be clearly identified, and, due to the continuity of the spectrum, smoothly transition from one color to another.

It is believed that certain colors are situated in certain range of wavelengths. This is illustrated in Table 1.

Light wavelengths

Table 1

For photographers, the distribution of wavelengths over the zones of the spectrum is of particular interest.

In total there are three spectrum zones: Blue ( B lue), green ( G reen) and Red ( R ed).

By the first letters of English words R ed (red), G rein (green), B lue (blue) is called the color representation system - RGB.

AT RGB- the system operates a lot of devices connected by graphic information, for example, digital cameras, displays, etc.

The wavelengths of monochromatic radiations, distributed over the zones of the spectrum, are presented in Table 2.

When working with tables it is important to take into account the continuous nature of the spectrum. It is the continuous nature of the spectrum that leads to a discrepancy, both in the width of the visible radiation spectrum and in the position of the boundaries of the spectral colors.

Wavelengths of monochromatic radiations distributed over spectrum zones

table 2

As for monochromatic colors, different researchers allocate a different amount of them! It is customary to count from six to eight different colors of the spectrum.

Six colors of the spectrum

Table 3

When highlighting seven colors of the spectrum it is proposed from the blue range of 436-495 nm, see Table 3, to distinguish two components, one of which has a blue (440-485 nm), the other has a blue (485-500 nm) color.

Seven colors of the spectrum

Table 4

The names of the seven colors of the spectrum are given in Table 5.

Names of the seven colors of the spectrum

Table 5

When highlighting eight colors of the spectrum stand out separately yellow green(550-575 nm) by reducing the range green and yellow colors respectively.

Eight colors of the spectrum

Table 6

For various purposes, researchers can distinguish another (much larger) number of spectrum colors. However, for practical purposes, photographers tend to limit themselves to 6-8 colors.

Primary and secondary colors

Fig.1. Black and white, primary and secondary colors

Primary colors- This three colors from which you can get any other colors.

Actually, modern digital photography is based on this principle, using red (R), green (G) and blue (B) as primary colors, see Table 7.

Additional colors are colors that, when mixed with primary colors, produce white. see Table 7.

Table 7

Main color	Complementary color	Resulting Color
RGB (0 0 225) Blue/Blue	RGB (255 225 0) Yellow	RGB (255 225 225) White
RGB (0 225 0) Green/Green	RGB (255 0 225) Purple or Fuchsia/Magenta	RGB (255 225 225) White
RGB (255 0 0) Red	RGB (0 225 225) Blue/Cyan	RGB (255 225 225) White