A straight line perpendicular to a set of points of equal phase is called. Intersection point of non-parallel lines

Lines defined by general equations: and

Given lines are parallel if and only if

Straight lines on the plane, given in the form:
And
are perpendicular only when
(at
). These lines are parallel if and only if their slopes are equal, i.e.

Lines defined by their canonical equations:
And
mutually perpendicular if and only if
These lines are parallel if the following condition is met:

2.7. Intersection point of non-parallel lines

If two lines are given on a plane:
And
, then according to statement 2 coordinates
the intersection points of these lines can be calculated using the formulas:

Lecture 10. Line in space

General equation of a line

direction vector straight

Canonical equation of the line

Parametric equations of a line

Equation of a line passing through 2 given points

And lie in the same plane

Straight line and plane in space

L- lies in the plane

3.
If

Lecture 11. Second order curves

A second-order curve is the geometric locus of points specified by the equation: . Depending on the type of this curve, the equation can be reduced to one of the canonical ones, defining a curve belonging to one of the classes.

Classification of second order curves

Non-degenerate Degenerate

Hyperbola

Parabola

Dot (0;0)

Pair of intersecting lines

Pair of coincident lines

Pair of parallel lines

Canonical equation

Canonical equation
or

Canonical equation

Sign of degeneracy of a curve: the equation can be represented as a product of two factors.

Second order curve given by the canonical equation
, is called an ellipse. a, b – semi-axes of the ellipse. If
, That a- semi-major axis, b- minor axis.

Construction of an ellipse given by the canonical equation
. Let the equation of the ellipse have the form
. Let's construct linesx= 6 and y= 3 . The points of intersection of these lines with the coordinate axes belong to the ellipse. Let's connect them with a smooth curve and get the desired graph. Usually an ellipse is defined as the locus of points, the sum of the distances from which to the foci of the ellipse is a constant value and equal to 2 a. The focal coordinates from the ellipse equation are found using the formulas
if in the equation
. If
, then the foci have coordinates
(the ellipse is oriented vertically).

The optical property of an ellipse is that if a point source of light is placed at one focus of the ellipse, then its image will appear at the other focus.

The eccentricity of an ellipse is the degree of its elongation - the ratio of the distance from the center of the ellipse to the focus to its semi-major axis, calculated by the formula . For an ellipse in general case>1, if , then the ellipse turns into a circle. For an ellipse given by the equation
eccentricity
, and the foci are at the points
.

Circumference – special case ellipse, given by the equation
, Where R– radius of the circle. The circle has 0, and its foci coincide with the center (origin).

Hyperbola

Hyperbola – a curve defined by the canonical equation
or
.a, b are the semiaxes of the hyperbola. The semi-axis near which there is a “+” sign in the equation is called real. Direct
- asymptotes of a hyperbola (the graph tends to them, but never reaches them).

Construction of a hyperbola

Construction of a hyperbola, given by the equation we start with the deposition along the Ox axis of a segment of length a units, and along the Oy axis – length b units. Building straight lines
And
. The hyperbola will touch the resulting rectangle at two points
. Let's draw straight lines
- asymptotes of a hyperbola. Let's take a couple more points to more accurately determine the shape of the curve (the more points, the better). Type of curve (for example, the hyperbola given by the equation is taken
) is shown in the figure. If the equation contains hyperbolas
change the signs of x and y, then we get its conjugate hyperbola
, which has the same asymptotes.

Just like an ellipse, a hyperbola can be defined as the locus of points whose distance difference from the foci is constant. The foci of a hyperbola have coordinates
, Where
(values a, b are taken from the hyperbola equation). A hyperbola conjugate to a given one will have foci at the points
.

The optical property of a hyperbola is that if a light source is placed at one focus of the hyperbola, then from a point at infinity it will be visible as if it were at the second focus.

The eccentricity of a hyperbola is the degree of its elongation. For a hyperbola (in the general case >1) given by the equation
eccentricity
, and the foci are at the points
.

Parabola

A parabola is a second-order curve defined by a canonical equation of the form
or
, Where p– parameter of the parabola. Depending on the type of equation and the value of the parameter, the branches of the parabola can be directed:

A parabola can be defined as the locus of points equidistant from a point
- focus - and direct
- headmistresses.

The optical property of a parabola is that if a point source of light is placed at the focus of the parabola, then a parallel beam of rays will emerge from it.

Reducing equations of second-order curves to canonical form.

The general equation of the curve is , and we accept (to simplify calculations) B = 0. There are two methods for transforming the equation general view to canonical:

Selecting a complete square

Variable replacement

For this equation, it is convenient to introduce a replacement in the form:

, Where x’ And y’ – new variables.

If A and C are not equal to 0, then
- new center second order curve, and x’ And y’ - new axles.

1. A second-order curve is given by the equation
. Find out what it corresponds to.

This equation corresponds to a circle with a displaced center, which has a canonical equation, where ( x 0 ;y 0) are the coordinates of the center of the circle, and R is its radius. Let's use the selection method full square to find the canonical form of the equation.

So, this equation corresponds to a circle of radius 2 units. with center at point (2;0).

Reduce the equation to canonical form and plot the curve:

Let's use the variable replacement method. We have:

The result is a canonical equation of an ellipse with center at point (1;-2). We build it according to the algorithm described above.

We use the method of isolating a complete square and replacing a variable.

The result is an equation of a parabola with center at the point (-2;2)

So far we have been doing geometric optics and studied the propagation of light rays. At the same time, we considered the concept of a ray to be intuitively clear and did not give it a definition. The basic laws of geometric optics were formulated by us as postulates.
Now we'll get down to business wave optics, in which light is treated as electromagnetic waves. Within the framework of wave optics, the concept of a ray can already be strictly defined. Basic postulate wave theory is Huygens' principle; the laws of geometric optics turn out to be its consequences.

Wave surfaces and rays.

Imagine a small light bulb that produces frequent periodic flashes. Each flash generates a divergent light wave in the form of an expanding sphere (centered on a light bulb). Let us stop time and see in space the stopped spheres of light formed by flashes at various previous moments in time.

These spheres are the so-called wave surfaces. Notice that the rays coming from the light bulb are perpendicular to the wave surfaces.

To give a strict definition of a wave surface, let's first remember what the oscillation phase is. Let the quantity perform harmonic oscillations according to the law:

So, phase is the quantity that is the argument of the cosine. The phase, as we see, increases linearly with time. The phase value at is equal and is called
initial phase.

Let us also remember that a wave represents the propagation of vibrations in space. In the case of mechanical waves, these will be vibrations of particles elastic medium, in the case of electromagnetic waves - oscillations of tension vectors electric field and magnetic field induction.

Regardless of which waves are considered, we can say that at each point in space captured by the wave process, oscillations of some magnitude occur; such a quantity is a set of coordinates of an oscillating particle in the case of a mechanical wave or a set of coordinates of vectors describing the electric and magnetic fields in an electromagnetic wave.

The phases of oscillations at two different points in space, generally speaking, have different meaning. Of interest are the sets of points at which the phase is the same. It turns out that the set of points at which the phase of oscillations in at the moment time has a fixed value and forms a two-dimensional surface in space.

Definition. wave surface - this is the set of all points in space at which the phase of oscillations at a given moment in time has the same value.

In short, wave surface is the constant phase surface. Each phase value has its own wave surface. A set of different phase values corresponds to a family of wave surfaces.

Over time, the phase at each point changes, and the wave surface corresponding to a fixed phase value moves in space. Therefore, the propagation of waves can be considered as the movement of wave surfaces! Thus, we have at our disposal convenient geometric images for describing physical wave processes.

For example, if a point light source is in a transparent homogeneous environment, then the wave surfaces are concentric spheres with common center in the source. The spread of light appears as an expansion of these spheres. We have already seen this above in the situation with the light bulb.

Only one wave surface can pass through each point in space at a given time. In fact, if we assume that two wave surfaces pass through a point, corresponding different meanings phases and , then we immediately obtain a contradiction: the phase of oscillations at a point will simultaneously be equal to these two different numbers.

Since a single wave surface passes through a point, then the direction of the perpendicular to the wave surface at a given point is also uniquely determined.

Definition. Beam - this is a line in space, which at each point is perpendicular to the wave surface passing through this point.

In other words, a ray is a common perpendicular to a family of wave surfaces. The direction of the beam is the direction of propagation of the wave. Along the rays, wave energy is transferred from one point in space to another.

As the wave propagates, the boundary moves, separating the region of space captured by the wave process and the region that is not yet disturbed. This boundary is called the wave front. Thus, wave front is the set of all points in space reached oscillatory process at a given moment in time. A wave front is a special case of a wave surface; this is, so to speak, the “very first” wave surface.

To the most simple types geometric surfaces include sphere and plane. Accordingly, we have two important cases of wave processes with wave surfaces of this shape - these are spherical and plane waves.

Spherical wave.

The wave is called spherical, if its wave surfaces are spheres (Fig. 1).

The wave surfaces are shown with a blue dotted line, and the green radial arrows are rays perpendicular to the wave surfaces.

Consider a transparent homogeneous medium, physical properties which are the same along all directions. A point source of light placed in such a medium emits spherical waves. This is understandable -
after all, light will travel in every direction at the same speed, so any wave surface will be a sphere.

Well light rays, as we noticed, turn out to be ordinary rectilinear in this case geometric rays starting at the source. Remember the law rectilinear propagation Sveta: in a transparent homogeneous medium, light rays are straight lines? In geometric optics we formulated it as a postulate. Now we see (for the case of a point source) how this law follows from the concepts of wave nature Sveta.

In the topic " Electromagnetic waves"we introduced the concept of radiation flux density:

Here is the energy that is transferred over time through the surface area located perpendicular to the rays. Thus, the radiation flux density is the energy transferred by a wave along the rays through a unit area per unit time.

In our case, the energy is uniformly distributed over the surface of the sphere, the radius of which increases as the wave propagates. The surface area of the sphere is equal to: , therefore for the radiation flux density we obtain:

As we see, The radiation flux density in a spherical wave is inversely proportional to the square of the distance to the source.

Since energy is proportional to the square of the vibration amplitude electromagnetic field, we come to the conclusion that the amplitude of oscillations in a spherical wave is inversely proportional to the distance to the source.

Plane wave.

The wave is called flat, if its wave surfaces are planes (Fig. 2).

Shown in blue dotted line parallel planes, which are wave surfaces. The rays - green arrows - again turn out to be straight lines.

The plane wave is one of the most important idealizations of wave theory; mathematically it is described most simply. This idealization can be used, for example, when we are at a sufficiently long distance from the source. Then, in the vicinity of the observation point, we can neglect the curvature of the spherical wave surface and consider the wave to be approximately flat.

In the future, deriving the laws of reflection and refraction from Huygens' principle, we will use plane waves. But first, let's deal with Huygens' principle itself.

Huygens' principle.

We said above that it is convenient to imagine the propagation of waves as the movement of wave surfaces. But according to what rules do wave surfaces move? In other words, how, knowing the position of the wave surface at a given moment in time, determine its position at the next moment?

The answer to this question is given by Huygens' principle - the main postulate of wave theory. Huygens' principle equally valid for both mechanical and electromagnetic waves.

To better understand Huygens' idea, let's look at an example. Let's throw a handful of stones into the water. Each stone will produce a circular wave with its center at the point where the stone falls. These circular waves, overlapping each other, will create an overall wave pattern on the surface of the water. The important thing is that all the circular waves and the wave pattern generated by them will exist even after the stones sink to the bottom. Therefore, direct cause the initial circular waves are not served by the stones themselves, but local disturbances the surface of the water in those places where the stones fell. It is local disturbances themselves that are the sources of diverging circular waves and the emerging wave pattern, and it is no longer so important what exactly caused each of these disturbances - whether it was a stone, a float or some other object. To describe the subsequent wave process, it is only important that circular waves arose at certain points on the surface of the water.

Huygens's key idea was that local disturbances can be generated not only by foreign objects such as a stone or a float, but also by a wave propagating in space!

Huygens' principle. Each point in space involved in wave process, itself becomes a source of spherical waves.

These spherical waves propagating in all directions from each point of wave disturbance are called secondary waves. The subsequent evolution of the wave process consists of the superposition of secondary waves emitted by all points to which the wave process has already managed to reach.

Huygens' principle gives a recipe for constructing a wave surface at an instant of time based on its known position at an instant of time (Fig. 3).

Namely, we consider each point of the original wave surface as a source of secondary waves. During the time, the secondary waves will travel a distance , where is the wave speed. From each point of the old wave surface we build spheres of radius ; the new wave surface will be tangent to all these spheres. They also say that the wave surface at any moment of time serves envelope families of secondary waves.

But, of course, to construct a wave surface, we are not obliged to take secondary waves emitted by points that necessarily lie on one of the previous wave surfaces. The desired wave surface will be the envelope of a family of secondary waves emitted by points of any surface involved in the oscillatory process.

On the basis of Huygens' principle, we can derive the laws of reflection and refraction of light, which we previously considered only as a generalization of experimental facts.

Derivation of the law of reflection.

Let us assume that on the interface between two media falls plane wave(Fig. 4). We fix two points of this surface.

Two incident rays and arrive at these points; the plane perpendicular to these rays is the wave surface of the incident wave.

The normal to the reflecting surface is drawn at the point. The angle is, as you remember, the angle of incidence.

Reflected rays and come out from points I. The plane perpendicular to these rays is the wave surface of the reflected wave. Let us denote the angle of reflection for now; we want to prove that .

All points of the segment serve as sources of secondary waves. First of all, the wave surface reaches the point. Then, as the incident wave moves, other points are involved in the oscillatory process this segment, and last but not least - period.

Accordingly, the emission of secondary waves begins first at the point ; a spherical wave with center at has in Fig. 4 largest radius. As we approach the point, the radii of spherical secondary waves emitted by intermediate points decrease to zero - after all, the secondary wave will be emitted later, the closer its source is to the point.

The wave surface of the reflected wave is a plane tangent to all these spheres. In our planimetric drawing there is a tangent segment drawn from the point to the great circle with center at and radius .

Now note that the radius is the distance traveled by the secondary wave with center at while the wave surface moves to the point. Let's say this a little differently: the time of movement of the secondary wave from point to point is equal to the time of movement of the incident wave from point to point. But the speeds of movement of the incident and secondary waves coincide - after all, this is happening in the same medium! Therefore, since the speeds and times coincide, then the distances are equal: .

It turns out that right triangles are equal in hypotenuse and leg. Therefore, equal and corresponding sharp corners: . It remains to note that (since both of them are equal) and (both of them are equal).
Thus, is the angle of reflection equal to angle falls, which is what was required.

In addition, from the construction in Fig. 4 it is easy to see that the second statement of the law of refraction is also satisfied: the incident ray, the reflected ray and the normal to the reflecting surface lie in the same plane.

Derivation of the law of refraction.

Now we will show how the law of refraction follows from Huygens' principle. For definiteness, we will assume that a plane electromagnetic wave propagates in the air and falls on the boundary with some transparent medium (Fig. 5). As usual, the angle of incidence is the angle between the incident ray and the normal to the surface, the angle of refraction is the angle between the refracted ray and the normal.

The point is the first point of the segment that the wave surface of the incident wave reaches; at the point, the emission of secondary waves begins earliest. Let be the time that from this moment it takes the incident wave to reach the point, that is, to travel the segment.

Let's denote the speed of light in air, and let the speed of light in the medium be . While the incident wave travels a distance and reaches a point, a secondary wave from the point will spread to a distance.

Because , then . As a result, the wave surface not parallel wave surface - light refraction occurs! Within the framework of geometric optics, no explanation was given as to why the phenomenon of refraction was observed at all. The reason for refraction lies in the wave nature of light and becomes understandable from the point of view
Huygens' principle: the whole point is that the speed of secondary waves in the medium is less than the speed of light in air, and this leads to a rotation of the wave surface relative to its original position.

From right triangles and it is easy to see that and (for brevity, denoted ). We thus have:

Dividing these equations by each other, we get:

The ratio of the sine of the angle of incidence to the sine of the angle of refraction turned out to be equal to constant value, independent of the angle of incidence. This quantity is called the refractive index of the medium:

The result is the well-known law of refraction:

Please note: physical meaning the refractive index (as the ratio of the speeds of light in a vacuum and in a medium) was clarified again thanks to Huygens’ principle.

From Fig. 5, the second statement of the law of refraction is also obvious: the incident ray, the refracted ray and the normal to the interface lie in the same plane.

The same body can simultaneously participate in two or more movements. A simple example is the motion of a ball thrown at an angle to the horizontal. We can assume that the ball participates in two independent mutually perpendicular movements: uniform horizontally and uniformly variable vertically. Same body ( material point) can participate in two (or more) oscillatory movements.

Under addition of oscillations understand the definition of the law of resultant oscillation if oscillatory system simultaneously participates in several oscillatory processes. There are two limiting cases - the addition of oscillations in one direction and the addition of mutual perpendicular vibrations.

2.1. Addition of harmonic vibrations of one direction

1. Addition of two oscillations of the same direction(co-directional oscillations)

can be done using the vector diagram method (Figure 9) instead of adding two equations.

Figure 2.1 shows the amplitude vectors A 1(t) and A 2 (t) added oscillations at an arbitrary moment of time t, when the phases of these oscillations are respectively equal And . The addition of oscillations comes down to the definition . Let's take advantage of the fact that vector diagram the sum of the projections of the vectors being added is equal to the projection of the vector sum of these vectors.

The resulting oscillation corresponds in the vector diagram to the amplitude vector and phase.

Figure 2.1 – Addition of co-directional oscillations.

Vector magnitude A(t) can be found using the cosine theorem:

The phase of the resulting oscillation is given by the formula:

If the frequencies of the added oscillations ω 1 and ω 2 are not equal, then both the phase φ(t) and the amplitude A(t) The resulting fluctuations will change over time. Added oscillations are called incoherent in this case.

2. Two harmonic vibrations x 1 and x 2 are called coherent, if their phase difference does not depend on time:

But since, in order to fulfill the condition of coherence of these two oscillations, their cyclic frequencies must be equal.

The amplitude of the resulting oscillation obtained by adding codirectional oscillations with equal frequencies(coherent oscillations) is equal to:

The initial phase of the resulting oscillation is easy to find if you project the vectors A 1 and A 2 on coordinate axes OX and OU (see Figure 9):

So, the resulting oscillation obtained by adding two harmonic co-directional oscillations with equal frequencies is also a harmonic oscillation.

3. Let us study the dependence of the amplitude of the resulting oscillation on the difference in the initial phases of the added oscillations.

If , where n is any non-negative integer

(n = 0, 1, 2…), then minimum. The added oscillations at the moment of addition were in antiphase. When the resulting amplitude is zero.

If , That , i.e. the resulting amplitude will be maximum. At the moment of addition, the added oscillations were in one phase, i.e. were in phase. If the amplitudes of the added oscillations are the same , That .

4. Addition of co-directional oscillations with unequal but similar frequencies.

The frequencies of the added oscillations are not equal, but the frequency difference much less than both ω 1 and ω 2. The condition for the proximity of the added frequencies is written by the relations.

An example of the addition of co-directional oscillations with similar frequencies is the movement of a horizontal spring pendulum, the spring stiffness of which is slightly different k 1 and k 2.

Let the amplitudes of the added oscillations be the same , and the initial phases are equal to zero. Then the equations of the added oscillations have the form:

, .

The resulting oscillation is described by the equation:

The resulting oscillation equation depends on the product of two harmonic functions: one – with frequency , the other with frequency , where ω is close to the frequencies of the added oscillations (ω 1 or ω 2). The resulting oscillation can be considered as harmonic oscillation from changing to harmonic law amplitude. This oscillatory process is called beats. Strictly speaking, the resulting oscillation in the general case is not a harmonic oscillation.

Absolute value cosine is taken because the amplitude is a positive quantity. The nature of the dependence x res. during beating is shown in Figure 2.2.

Figure 2.2 – Dependence of displacement on time during beating.

The amplitude of the beats changes slowly with frequency. The absolute value of the cosine is repeated if its argument changes by π, which means that the value of the resulting amplitude will be repeated after a time interval τ b, called beat period(See Figure 12). The value of the beat period can be determined from the following relationship:

The value is the beating period.

Magnitude is the period of the resulting oscillation (Figure 2.4).

2.2. Addition of mutually perpendicular vibrations

1. A model on which the addition of mutually perpendicular oscillations can be demonstrated is presented in Figure 2.3. A pendulum (a material point of mass m) can oscillate along the OX and OU axes under the action of two elastic forces directed mutually perpendicularly.

Figure 2.3

The folded oscillations have the form:

The oscillation frequencies are defined as , , where , are the spring stiffness coefficients.

2. Consider the case of adding two mutually perpendicular oscillations with the same frequencies , which corresponds to the condition (identical springs). Then the equations of the added oscillations will take the form:

When a point is involved in two movements simultaneously, its trajectory can be different and quite complex. The equation for the trajectory of the resulting oscillations on the OXY plane when adding two mutually perpendicular ones with equal frequencies can be determined by eliminating original equations for x and y time t:

The type of trajectory is determined by the difference in the initial phases of the added oscillations, which depend on initial conditions(see § 1.1.2). Let's consider the possible options.

a) If , where n = 0, 1, 2…, i.e. the added oscillations are in phase, then the trajectory equation will take the form:

(Figure 2.3 a).


Figure 2.3.a	Figure 2.3 b

b) If (n = 0, 1, 2...), i.e. the added oscillations are in antiphase, then the trajectory equation is written as follows:

(Figure 2.3b).

In both cases (a, b), the resulting movement of the point will be an oscillation along a straight line passing through point O. The frequency of the resulting oscillation is equal to the frequency of the added oscillations ω 0, the amplitude is determined by the relation.

Place of work: Municipal Educational Institution "Pokrovskaya Secondary School of Oktyabrsky District"

Position: physics teacher

Additional information: the test is designed according to the content general education program for 11th grade high school

Option #1

The process of detecting objects using radio waves is called...

The process of isolating a low-frequency signal is called...

A. modulation B. radar C. Detection D. Scanning

A straight line perpendicular to a set of points equal phase called...

B. for object detection;

A. beam B. wave front C. wave surface

The wave front is...

A. last wave surface B. first wave surface

B. Any wave surface

A. beam B. wave front C. wave surface

What formula is used to determine the distance to an object during radar?

Test No. 3 “Electromagnetic waves. Radio"

Option No. 2

What is the detection process for?

A. to transmit a signal to long distances;

B. for object detection;

B. To highlight a low-frequency signal;

D. To convert a low-frequency signal.

How to increase the frequency of an oscillatory circuit?

A. it is necessary to reduce the capacitance of the capacitor and increase the inductance of the oscillatory circuit;

B. it is necessary to increase the capacitance of the capacitor and reduce the inductance of the oscillatory circuit;

B. It is necessary to reduce both the capacitance of the capacitor and the inductance of the oscillating circuit;

D. It is necessary to increase both the capacitance of the capacitor and the inductance of the oscillating circuit.

The process of changing high-frequency oscillations with the help of low-frequency oscillations is called...

A. modulation B. radar C. Detection D. Scanning

Electromagnetic waves are...

A. transverse B. longitudinal C. Both transverse and longitudinal at the same time

A. modulation B. radar C. Detection D. Scanning

A. R=2ct B. R=υt/2 C. R=ct/2 D. R=2υt

Broadcast sound signal carried out over long distances...

A. direct transmission of an audio signal without any transformations;

B. using a detected signal;

B. Using a simulated signal.

A. beam B. wave front C. wave surface

A. scanning B. radar C. Broadcasting D. Modulation E. detection

What device can be used to produce electromagnetic waves?

A. radio B. TV C. Oscillating circuit

D. Open oscillatory circuit

A set of points of the same phase is called...

The wave front is...

The set of points to which the disturbance has reached at time t is called...

A. beam B. wave front C. wave surface

Does the modulated signal carry information?

A. yes, but we don’t perceive it;

B. yes, and we can perceive it directly with our hearing organs;

How does the transmitting part of a radar work?

A. works constantly B. turns off spontaneously at any time

B. Turns off immediately after signal transmission

Electromagnetic waves travel at a speed equal to...

A. from any B. 3108mm/s C. 3108km/s D. 3108m/s

Test No. 3 “Electromagnetic waves. Radio"

Option #3

A. modulation B. radar C. Detection D. Scanning

What is the detection process for?

A. for transmitting signals over long distances;

B. for object detection;

B. To highlight a low-frequency signal;

D. To convert a low-frequency signal.

Does the modulated signal carry information?

A. yes, but we don’t perceive it;

B. yes, and we can perceive it directly with our hearing organs;

Electromagnetic waves are...

A. transverse B. longitudinal C. Both transverse and longitudinal at the same time

The process of isolating a low frequency signal is called….

A. modulation B. radar C. Detection D. Scanning

What formula is used to determine the distance to objects?

A. R=2ct B. R=υt/2 C. R=ct/2 D. R=2υt

The transmission of sound signals over long distances is carried out...

A. direct transmission of an audio signal without any transformations;

B. using a detected signal;

B. Using a simulated signal.

How to reduce the frequency of an oscillatory circuit?

A. it is necessary to reduce the capacitance of the capacitor and increase the inductance of the oscillatory circuit;

B. it is necessary to increase the capacitance of the capacitor and reduce the inductance of the oscillatory circuit;

B. It is necessary to reduce both the capacitance of the capacitor and the inductance of the oscillating circuit;

D. It is necessary to increase both the capacitance of the capacitor and the inductance of the oscillating circuit.

The process of detecting objects using radio waves is called...

A. scanning B. radar C. Broadcasting D. Modulation E. detection

What device can be used to produce electromagnetic waves?

A. radio B. TV C. Oscillating circuit

D. Open oscillatory circuit

A set of points of the same phase is called...

A. beam B. wave surface C. wave front

A straight line perpendicular to a set of points of equal phase is called...

A. beam B. wave front C. wave surface

Electromagnetic waves travel at a speed equal to...

A. from any B. 3108mm/s C. 3108km/s D. 3108m/s

The wave front is...

A. last wave surface B. any wave surface

B. First wave surface

The set of points to which the disturbance has reached at time t is called...

A. beam B. wave front C. wave surface

How does the receiving part of a radar work?

A. works constantly B. turns off spontaneously at any time

V. turns on immediately after signal transmission

Test No. 3 “Electromagnetic waves. Radio"

Option No. 4

The process of detecting objects using radio waves is called...

A. scanning B. radar C. Broadcasting D. Modulation E. detection

A set of points of the same phase is called...

A. beam B. wave surface C. wave front

What device can be used to produce electromagnetic waves?

A. radio B. TV C. Oscillating circuit

D. Open oscillatory circuit

The process of changing high-frequency oscillations with the help of low-frequency oscillations is called...

A. modulation B. radar C. Detection D. Scanning

How does the transmitting part of a radar work?

A. works constantly B. turns off spontaneously at any time

B. Turns off immediately after signal transmission

What formula is used to determine the distance to objects?

A. R=2ct B. R=υt/2 C. R=ct/2 D. R=2υt

The process of isolating a low frequency signal is called….

A. modulation B. radar C. Detection D. Scanning

Does the detected signal carry information?

A. yes, but we don’t perceive it;

B. yes, and we can perceive it directly with our hearing organs;

The transmission of sound signals over long distances is carried out...

A. direct transmission of an audio signal without any transformations;

B. using a detected signal;

B. Using a simulated signal.

How to reduce the oscillation period of an oscillating circuit?

A. it is necessary to reduce the capacitance of the capacitor and increase the inductance of the oscillatory circuit;

B. it is necessary to increase the capacitance of the capacitor and reduce the inductance of the oscillatory circuit;

B. It is necessary to reduce both the capacitance of the capacitor and the inductance of the oscillating circuit;

D. It is necessary to increase both the capacitance of the capacitor and the inductance of the oscillating circuit.

A straight line perpendicular to a set of points of equal phase is called...

A. beam B. wave front C. wave surface

What is the modulation process for?

A. for transmitting signals over long distances;

B. for object detection;

B. To highlight a low-frequency signal;

D. To convert a low-frequency signal.

Electromagnetic waves are...

A. transverse B. longitudinal C. Both transverse and longitudinal at the same time

The wave front is...

A. last wave surface B. any wave surface

B. First wave surface

The set of points to which the disturbance has reached at time t is called...

A. beam B. wave front C. wave surface

Electromagnetic waves travel at a speed equal to...

A. from any B. 3108mm/s C. 3108km/s D. 3108m/s

References:

Physics: Textbook. for 11th grade general education institutions / G. Ya. Myakishev, B. B. Bukhovtsev. - 15th ed. - M.: Education, 2015.-381 p.

Physics. Problem book. 10-11 grades: A manual for general education. institutions / Rymkevich A.P. - 12th ed., stereotype. - M.: Bustard, 2008. - 192 p.

Independent and tests. Physics. Kirik, L. A P.-M.: Ilexa, 2005.