The waves that we are used to seeing on the surface of the sea are formed mainly by the action of the wind. However, waves can also occur for other reasons, then they are called;
Tidal, formed under the action of the tide-forming forces of the Moon and the Sun;
Baric, arising from sudden changes in atmospheric pressure;
Seismic (tsunami), resulting from an earthquake or volcanic eruptions;
Shipborne, arising from the movement of the vessel.
Wind waves are predominant on the surface of the seas and oceans. Tidal, seismic, baric and ship waves do not have a significant effect on the navigation of ships in the open ocean, so we will not dwell on their description. Wind waves are one of the main hydrometeorological factors that determine the safety and economic efficiency of navigation, since a wave, running into a ship, falls on it, sways, hits the side, floods the decks and superstructures, and reduces the speed. The pitching creates dangerous rolls, makes it difficult to determine the position of the vessel and greatly exhausts the crew. In addition to the loss of speed, the wave causes the ship to yaw and evade from a given course, and constant rudder shifting is required to keep it.
Wind waves are the process of formation, development and propagation of wind-induced waves on the sea surface. Wind waves have two main features. The first feature is irregularity: the disorder of the sizes and shapes of the waves. One wave does not repeat another, a large one can be followed by a small one, and maybe even a larger one; each individual wave continuously changes its shape. Wave crests move not only in the direction of the wind, but also in other directions. Such a complex structure of the disturbed sea surface is explained by the eddy, turbulent nature of the wind that forms the waves. The second feature of the wave is the rapid variability of its elements in time and space and is also associated with the wind. However, the size of the waves depends not only on the speed of the wind, the duration of its action, the area and configuration of the water surface are essential. From the point of view of practice, it is not necessary to know the elements of each individual wave or each wave oscillation. Therefore, the study of waves is ultimately reduced to the identification of statistical patterns, which are numerically expressed by the dependencies between the elements of the waves and the factors that determine them.
3.1.1. Wave elements
Each wave is characterized by certain elements,Common elements for waves are (Fig. 25):
Top - the highest point of the wave crest;
Sole - the lowest point of the hollow of the wave;
Height (h) - excess of the top of the wave;
Length (L) is the horizontal distance between the tops of two adjacent crests on a wave profile drawn in the general direction of wave propagation;
Period (t) - the time interval between the passage of two adjacent wave tops through a fixed vertical; in other words, it is the time interval during which the wave travels a distance equal to its length;
Steepness (e) - the ratio of the height of a given wave to its length. The steepness of the wave at different points of the wave profile is different. The average steepness of the wave is determined by the ratio:
Rice. 25. Basic elements of waves.
For practice, the greatest slope is important, which is approximately equal to the ratio of the wave height h to its half-length λ/2
- wave speed c - the speed of the wave crest in the direction of its propagation, determined for a short time interval of the order of the wave period;
Wave front - a line on the plan of a rough surface, passing along the tops of the crest of a given wave, which are determined by a set of wave profiles drawn parallel to the general direction of wave propagation.
For navigation, such elements of waves as height, period, length, steepness and general direction of wave movement are of the greatest importance. All of them depend on the parameters of the wind flow (wind speed and direction), its length (acceleration) over the sea and the duration of its action.
Depending on the conditions of formation and propagation, wind waves can be divided into four types.
Wind - a system of waves, which is at the time of observation under the influence of the wind with which it is caused. The directions of propagation of wind waves and wind in deep water usually coincide or differ by no more than four points (45°).
Wind waves are characterized by the fact that their lee slope is steeper than the windward one, so the tops of the ridges usually collapse, forming foam, or even break off by a strong wind. When waves enter shallow water and approach the shore, the directions of wave and wind propagation can differ by more than 45°.
Swell - wind-induced waves propagating in a wave formation area after the wind weakens and / or changes its direction, or wind-induced waves that come from a wave formation region to another area where the wind blows with a different speed and / or direction. A special case of a swell that propagates in the absence of wind is called dead swell.
Mixed - excitement resulting from the interaction of wind waves and swell.
Transformation of wind waves - a change in the structure of wind waves with a change in depth. In this case, the shape of the waves is distorted, they become steeper and shorter, and at a shallow depth not exceeding the height of the wave, the crests of the latter overturn, and the waves are destroyed.
In their appearance, wind waves are characterized by different forms.
Ripples - the initial form of development of wind waves, arising under the influence of a weak wind; the crests of the waves with ripples resemble scales.
Three-dimensional excitement - a set of waves, the average length of the crest of which is several times greater than the average wavelength.
Regular wave - wave in which the form and elements of all waves are the same.
Crowd - chaotic excitement arising from the interaction of waves running in different directions.
Waves breaking over banks, reefs or rocks are called breakers. Waves breaking in the coastal zone are called surf. At steep coasts and at port facilities, the surf has the form of a reverse fault.
Waves on the surface of the sea are divided into free, when the force that caused them stops acting and the waves move freely, and forced, when the action of the force that caused the formation of waves does not stop.
According to the variability of wave elements in time, they are divided into steady, i.e., wind waves, in which the statistical characteristics of the waves do not change in time, and developing or damping - changing their elements in time.
According to the waveform, they are divided into two-dimensional - a set of waves, the average length of the crest of which is many times greater than the average wavelength, three-dimensional - a set of waves, the average length of the crest of which is several times greater than the wavelength, and solitary, having only a dome-shaped crest without a sole.
Depending on the ratio of the wavelength to the depth of the sea, waves are divided into short ones, the length of which is much less than the depth of the sea, and long waves, the length of which is greater than the depth of the sea.
By the nature of the movement of the waveform, they are translational, in which there is a visible movement of the waveform, and standing - not having movement. According to how the waves are located, they are divided into surface and internal. Internal waves are formed at one or another depth on the interface between water layers of different density.
3.1.2. Methods for calculating wave elements
When studying sea waves, some theoretical provisions are used to explain certain aspects of this phenomenon. The general laws of the structure of waves and the nature of the motion of their individual particles are considered by the trochoidal theory of waves. According to this theory, individual water particles in surface waves move along closed ellipsoidal orbits, making a complete revolution in a time equal to the wave period t.The rotational motion of successive water particles shifted by a phase angle at the initial moment of motion creates the appearance of translational motion: individual particles move in closed orbits, while the wave profile moves translationally in the direction of the wind. The trochoidal theory of waves made it possible to mathematically substantiate the structure of individual waves and to interconnect their elements. Formulas were obtained that make it possible to calculate the individual elements of the waves
where g is the free fall acceleration, Wave length K, its propagation velocity C and period t are interconnected by the dependence K=Cx.
It should be noted that the trochoidal theory of waves is valid only for regular two-dimensional waves, which are observed in the case of free wind waves - swells. With three-dimensional wind waves, the orbital paths of the particles are not closed circular orbits, since under the influence of the wind there is a horizontal transfer of water on the sea surface in the direction of wave propagation.
The trochoidal theory of sea waves does not reveal the process of their development and attenuation, as well as the mechanism of energy transfer from wind to wave. Meanwhile, the solution of precisely these issues is necessary in order to obtain reliable dependencies for calculating the elements of wind waves.
Therefore, the development of the theory of sea waves followed the path of developing theoretical and empirical relationships between wind and waves, taking into account the diversity of real sea wind waves and the non-stationarity of the phenomenon, i.e., taking into account their development and attenuation.
In general, the formulas for calculating the elements of wind waves can be expressed as a function of several variables
H, t, L, C \u003d f (W, D t, H),
Where W - wind speed; D - acceleration, t - duration of the wind action; H is the depth of the sea.
For shallow water areas of the seas, to calculate the height and wavelength, you can use the dependencies
Coefficients a and z are variable and depend on the depth of the sea
A \u003d 0.0151H 0.342; z = 0.104H 0.573 .
For open areas of the seas, the elements of waves, the height coverage of which is 5%, and the average values of the wavelengths are calculated according to the dependencies:
H = 0.45 W 0.56 D 0.54 A,
L \u003d 0.3lW 0.66 D 0.64 A.
Coefficient A is calculated by the formula
For open areas of the ocean, wave elements are calculated using the following formulas:
where e is the steepness of the wave at small accelerations, D PR is the maximum acceleration, km. The maximum height of storm waves can be calculated using the formula
where hmax - maximum wave height, m, D - acceleration length, miles.
At the State Oceanographic Institute, on the basis of the spectral statistical theory of waves, graphical relationships were obtained between wave elements and wind speed, the duration of its action and the length of the acceleration. These dependences should be considered the most reliable, giving acceptable results, on the basis of which nomograms were constructed at the Hydrometeorological Center of the USSR (V.S. Krasyuk) to calculate the height of the waves. The nomogram (Fig. 26) is divided into four quadrants (I-IV) and consists of a series of graphs arranged in a certain sequence.
In quadrant I (counted from the lower right corner) of the nomogram, a degree grid is given, each division of which (horizontally) corresponds to 1 ° meridian at a given latitude (from 70 to 20 ° N) for maps of a scale of 1:15 000000 polar stereographic projections. A degree grid is needed to convert the distance between isobars n and the radius of curvature of isobars R, measured on maps of a different scale, to a scale of 1:15 000000. In this case, we determine the distance between isobars n and the radius of curvature of isobars R in meridian degrees at a given latitude. The radius of curvature of the isobars R is the radius of the Circle with which the section of the isobar passing through the point for which the calculation is being carried out or near it has the greatest contact. It is determined with the help of a meter by selection in such a way that the arc drawn from the found center coincides with the given section of the isobar. Then, on the degree grid, we plot the measured values \u200b\u200bat a given latitude, expressed in degrees of the meridian, and with a compass solution we determine the radius of curvature of the isobars and the distance between the isobars, corresponding to a scale of 1: 15,000,000.
In quadrant II of the nomogram, curves are shown that express the dependence of wind speed on the pressure gradient and the geographical latitude of the place (each curve corresponds to a certain latitude - from 70 to 20 ° N). For the transition from the calculated gradient wind to the wind blowing near the sea surface (at a height of 10 m), a correction was derived that takes into account the stratification of the atmospheric surface layer. When calculating for the cold part of the year (stable stratification t w 2 ° C), the coefficient is 0.6.
Rice. Fig. 26. Nomogram for calculating the elements of waves and wind speed from maps of the surface pressure field, where isobars are drawn at intervals of 5 mbar (a) and 8 mbar (b). 1 - winter, 2 - summer.
Quadrant III takes into account the effect of isobar curvature on the geostrophic wind velocity. Curves corresponding to different values of the radius of curvature (1, 2, 5, etc.) are given by solid (winter) and dashed (summer) lines. The sign oo means that the isobars are rectilinear. Usually, when the radius of curvature exceeds 15°, no consideration of curvature is required in the calculations. The abscissa axis separating the yadrants III and IV determines the wind speed W for a given point.
In quadrant IV there are curves that make it possible to determine the height of the so-called significant waves (h 3H) with a probability of 12.5% by wind speed, acceleration or duration of the wind.
If it is possible to use not only data on wind speed, but also on the acceleration and duration of the wind when determining the height of the waves, the calculation is performed on the basis of the acceleration and duration of the wind (in hours). To do this, from quadrant III of the nomogram, we lower the perpendicular not to the acceleration curve, but to the curve of the duration of the wind action (6 or 12 hours). From the results obtained (acceleration and duration), the smaller value of the wave height is taken.
Calculation using the proposed nomogram can be made only for areas of the "deep sea", that is, for areas where the depth of the sea is not less than half the wavelength. For acceleration exceeding 500 km or wind duration greater than 12 h, the dependence of wave heights on wind corresponding to ocean conditions is used (thickened curve in quadrant IV).
Thus, to determine the height of the waves at a given point, it is necessary to perform the following operations:
A) find the radius of curvature of the isobar R passing through a given point or near it (using a compass by selection). The radius of curvature of isobars is determined only in the case of cyclonic curvature (in cyclones and troughs) and is expressed in meridian degrees;
B) determine the pressure difference n by measuring the distance between adjacent isobars in the area of the selected point;
C) according to the found values of R and n, depending on the season, we find the wind speed W;
D) knowing the wind speed W and acceleration D or the duration of the wind (6 or 12 hours), we find the height of significant waves (h 3H).
Acceleration is as follows. From each point for which the wave height is calculated, a streamline is drawn in the direction against the wind until its direction changes with respect to the initial one by an angle of 45 ° or reaches the coast or the ice edge. Approximately, this will be the acceleration or path of the wind, during which should be formed (waves arriving at a given point.
The duration of the action of the wind is defined as the time during which the direction of the wind is unchanged or deviates from the original by no more than ± 22.5 °.
According to the nomogram in Fig. 26a, one can determine the wave height from the map of the surface pressure field, on which the isobars are drawn through 5 mbar. If the isobars are drawn through 8 mbar, then the nomogram shown in fig. 26 b.
The period and wavelength can be calculated from the data on wind speed and wave height. An approximate calculation of the wave period can be made according to the graph (Fig. 27), which shows the relationship between the periods and the height of wind waves at different wind speeds (W). The wavelength is determined by its period and the depth of the sea at a given point according to the graph (Fig. 28).
Physics test Mechanical vibrations and waves Grade 9 with answers. The control work is presented in 4 versions, in each version there are 9 tasks.
Option 1
1. A load suspended on a spring made 300 oscillations in 1 minute. What is the frequency and period of oscillation of the load?
2. The vibration frequency of the tuning fork is 440 Hz. What is the wavelength of a sound wave from a tuning fork in air if the speed of sound propagation at 0 °C in air is 330 m/s?
3. According to the graph of harmonic oscillations (Fig. 125), determine the amplitude, period and frequency of oscillations.
4. How many oscillations did a mathematical pendulum make in 30 seconds if the frequency of its oscillations is 2 Hz? What is the period of its oscillations?
5. Determine the acceleration of gravity on the surface of Mars, provided that there a mathematical pendulum 50 cm long would make 40 oscillations in 80 s.
6. What is the speed of propagation of a sea wave if a person standing on the shore determines that the distance between two adjacent wave crests is 8 m and 45 wave crests pass by him in a minute?
7. How long does sound travel from one railway station to another along steel rails if the distance between them is 5 km, and the speed of sound propagation in steel is 500 m/s?
8. What is the ratio of the oscillation frequencies of two pendulums if their lengths are related as 1:4?
9. How will the period of oscillation of a mathematical pendulum change if it is transferred from the Earth to the Moon ( g Z \u003d 9.8 m / s 2; g L = 1.6 m/s 2)?
Option 2
1. A filament pendulum made 25 oscillations in 50 s. Determine the period and frequency of oscillation.
2. Determine at what distance from the observer the lightning struck if he heard thunder 3 s after he saw the lightning.
3. According to the graph (Fig. 126), determine the amplitude, period and frequency of oscillations.
4. What is the length of a mathematical pendulum that makes harmonic oscillations with a frequency of 0.5 Hz on the surface of the Moon? Acceleration of free fall on the surface of the Moon is 1.6 m/s 2 .
5. The length of the sea wave is 2 m. How many oscillations in 10 seconds will the float make on it if the wave propagation speed is 6 m / s?
6. How should the length of a mathematical pendulum be changed so that the period of its oscillations is reduced by 2 times?
7. Determine the length of a mathematical pendulum, which makes 4 complete oscillations less in 10 s than a mathematical pendulum 60 cm long.
8. One mathematical pendulum has a period of oscillation of 3 s, and the other has a period of 4 s. What is the period of oscillation of a mathematical pendulum whose length is equal to the sum of the lengths of the indicated pendulums?
9. What is the wavelength on water if the wave propagation speed is 2.4 m/s, and a body floating on water makes 30 oscillations in 25 s?
Option 3
1. The pendulum made 50 oscillations in 25 seconds. Determine the period and frequency of the pendulum's oscillations.
2. A radio beacon in the sea oscillates on waves with a period of 2 s. The speed of sea waves is 1 m/s. What is the wavelength?
3. According to the graph (Fig. 127), determine the amplitude, period and frequency of oscillations.
4. On an unknown planet, a pendulum 80 cm long made 36 complete oscillations in 1 minute. What is the free fall acceleration on this planet?
5. Determine the length of a wave propagating at a speed of 2 m / s, in which 10 oscillations occur in 20 s.
6. What is the length of a mathematical pendulum that makes 4 complete oscillations in 8 s?
7. How will the oscillation frequency of a thread pendulum 0.5 m long change if the length of the thread is increased by 1.5 m?
8. On the lake in calm weather, a heavy anchor was dropped from the boat. Waves started from the place of throwing. A person standing on the shore noticed that the wave reached him in 50 s, the distance between adjacent wave humps was 50 cm, and in 50 s there were 20 splashes against the shore. How far from shore was the boat?
9. Two pendulums are suspended from the ceiling. In the same time, one pendulum made 5 oscillations, and the other - 3 oscillations. What is the length of each pendulum if the difference between their lengths is 48 cm?
Option 4
1. What is the period of oscillation of the wave source if the wavelength is 2 m and its propagation speed is 5 m/s?
2. Determine the period and frequency of oscillation of a mathematical pendulum, which made 50 oscillations in 1 min 40 s.
3. According to the graph (Fig. 128), determine the amplitude, period and frequency of oscillations.
4. Determine how many oscillations on a sea wave an inflatable rubber boat will make in 20 s if the wave propagation speed is 4 m/s and its length is 4 m.
5. Determine how many times you need to increase the length of the mathematical pendulum so that the frequency of its oscillations decreases by 4 times.
6. Will the period of oscillation of the mass on the spring change if the iron mass is replaced by aluminum of the same size?
7. The periods of oscillation of two mathematical pendulums are related as 3:2. Calculate how many times the first pendulum is longer than the second.
8. A small ball is suspended on a thread 1 m long from the ceiling of the car. At what speed of the car will the ball vibrate especially strongly under the impact of the wheels on the rail joints? Rail length 12.5 m.
9. The distance between the wave crests in the sea is 5 m. When the boat moves on the opposite side, the wave hits the boat hull 4 times in 1 s, and 2 times when passing. Find the velocities of the boat and the wave if it is known that the speed of the boat is greater than the speed of the wave.
Answers to the test in physics Mechanical oscillations and waves Grade 9
Option 1
1. 5Hz, 0.2s
2. 0.75 m
3. 5 cm, 4 s, 0.25 Hz
4. 60, 0.5 s
5. 5 m/s 2
6. 6 m/s
7. 10 s
8. 2:1
9. T W / T L = 0.4
Option 2
1. 2 s, 0.5 Hz
2. 1 km
3. 10 cm, 2 s, 0.5 Hz
4. 0.16 m
5. 30
6. Reduce by 4 times
7. 4 m
8.5 s
9.2 m
Option 3
1. 0.5 s, 2 Hz
2. 2 m
3. 0.4m, 0.4s, 25Hz
4. 11.4 m/s 2
5. 4 m
6. 1 m
7. Decrease by 2 times
8. 100 m
9. 27 cm, 75 cm
Option 4
1. 0.4 s
2. 2 s, 0.5 Hz
3. 0.1m, 1s, 1Hz
4. 20 swings
5. 16 times
6. Reduced by 1.7 times
7. 2.25 times
8. 6.2 m/s
9. 15m/s, 5m/s
During the lesson, you will be able to independently study the topic “Wavelength. Wave propagation speed. In this lesson, you will learn about the special characteristics of waves. First of all, you will learn what a wavelength is. We will look at its definition, how it is labeled and measured. Then we will also look at the propagation speed of the wave in detail.
To begin with, let's remember that mechanical wave is an oscillation that propagates over time in an elastic medium. Since this is an oscillation, the wave will have all the characteristics that correspond to the oscillation: amplitude, oscillation period and frequency.
In addition, the wave has its own special characteristics. One of these characteristics is wavelength. Wavelength is denoted by the Greek letter (lambda, or they say "lambda") and is measured in meters. We list the characteristics of the wave:
What is a wavelength?
Wavelength - this is the smallest distance between particles that oscillate with the same phase.
Rice. 1. Wavelength, wave amplitude
It is more difficult to talk about the wavelength in a longitudinal wave, because it is much more difficult to observe particles that make the same vibrations there. But there is also a characteristic wavelength, which determines the distance between two particles making the same oscillation, oscillation with the same phase.
Also, the wavelength can be called the distance traveled by the wave in one period of particle oscillation (Fig. 2).
Rice. 2. Wavelength
The next characteristic is the speed of wave propagation (or simply the speed of the wave). Wave speed It is denoted in the same way as any other speed by a letter and is measured in. How to clearly explain what is the speed of the wave? The easiest way to do this is with a transverse wave as an example.
transverse wave is a wave in which perturbations are oriented perpendicular to the direction of its propagation (Fig. 3).
Rice. 3. Shear wave
Imagine a seagull flying over the crest of a wave. Its flight speed over the crest will be the speed of the wave itself (Fig. 4).
Rice. 4. To the determination of the wave speed
Wave speed depends on what is the density of the medium, what are the forces of interaction between the particles of this medium. Let's write down the relationship between the wave speed, wavelength and wave period: .
Speed can be defined as the ratio of the wavelength, the distance traveled by the wave in one period, to the period of oscillation of the particles of the medium in which the wave propagates. In addition, remember that the period is related to the frequency as follows:
Then we get a relation that relates the speed, wavelength and frequency of oscillations: .
We know that a wave arises as a result of the action of external forces. It is important to note that when a wave passes from one medium to another, its characteristics change: the speed of the wave, the wavelength. But the oscillation frequency remains the same.
Bibliography
- Sokolovich Yu.A., Bogdanova G.S. Physics: a reference book with examples of problem solving. - 2nd edition redistribution. - X .: Vesta: publishing house "Ranok", 2005. - 464 p.
- Peryshkin A.V., Gutnik E.M., Physics. Grade 9: textbook for general education. institutions / A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.
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Homework
