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 wavelength is. We will look at its definition, how it is designated and measured. Then we will also take a closer look at the speed of wave propagation.
To begin with, let us remember that mechanical wave is a vibration that propagates over time in an elastic medium. Since it is an oscillation, the wave will have all the characteristics that correspond to an oscillation: amplitude, oscillation period and frequency.
In addition, the wave has its own special characteristics. One of these characteristics is wavelength. The wavelength is denoted by the Greek letter (lambda, or they say “lambda”) and is measured in meters. Let us list the characteristics of the wave:
What is wavelength?
Wavelength - this is the smallest distance between particles vibrating with the same phase.
Rice. 1. Wavelength, wave amplitude
It is more difficult to talk about wavelength in a longitudinal wave, because there it is much more difficult to observe particles that perform the same vibrations. But there is also a characteristic - wavelength, which determines the distance between two particles performing the same vibration, vibration with the same phase.
Also, the wavelength can be called the distance traveled by the wave during one period of oscillation of the particle (Fig. 2).
Rice. 2. Wavelength
The next characteristic is the speed of wave propagation (or simply wave speed). Wave speed denoted in the same way as any other speed, by a letter and measured in . How to clearly explain what wave speed is? The easiest way to do this is using a transverse wave as an example.
Transverse wave is a wave in which disturbances are oriented perpendicular to the direction of its propagation (Fig. 3).
Rice. 3. Transverse 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 determine the wave speed
Wave speed depends on what the density of the medium is, what the forces of interaction between the particles of this medium are. Let's write down the relationship between wave speed, wave length and wave period: .
Velocity can be defined as the ratio of the wavelength, the distance traveled by the wave in one period, to the period of vibration of the particles of the medium in which the wave propagates. In addition, remember that the period is related to frequency by the following relationship:
Then we get a relationship that connects speed, wavelength and oscillation frequency: .
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 waves, 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 repartition. - X.: Vesta: publishing house "Ranok", 2005. - 464 p.
- Peryshkin A.V., Gutnik E.M., Physics. 9th grade: textbook for general education. institutions / A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.
- Internet portal "eduspb" ()
- Internet portal "eduspb" ()
- Internet portal “class-fizika.narod.ru” ()
Homework
Under wave speed understand the speed of propagation of disturbance. For example, a blow to the end of a steel rod causes local compression in it, which then spreads 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 the wave propagates. When a wave passes from one medium to another, its speed changes.
Wavelength is the distance over which a wave propagates in a time equal to the period of oscillation in it.
Since the speed of a 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:
Where v— wave speed, T- period of oscillations in the wave, λ (Greek letter lambda) - wavelength.
The formula expresses the relationship between wavelength and its speed and period. Considering that the period of oscillation in a wave is inversely proportional to the frequency v, i.e. T= 1/ v, we can obtain a formula expressing the relationship between wavelength and its speed and frequency:
,
where
The resulting formula shows that the wave speed is equal to the product of the wavelength and the frequency of oscillations in it.
Wavelength is the spatial period of the wave. In the wave graph (fig. above), the wavelength is defined as the distance between the two nearest harmonic points traveling wave, being in the same oscillation phase. These are like instant photographs of waves in an oscillating elastic medium at moments in time t And t + Δt. Axis X coincides with the direction of wave propagation, displacements are plotted on the ordinate axis s vibrating particles of the medium.
The frequency of oscillations in the wave coincides with the frequency of oscillations of the source, since the oscillations of particles in the medium are forced and do 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.
Wavelength
Examples
Approximately, with an error of about 0.07%, you can calculate the radio wavelength as follows: 300 divided by the frequency in megahertz, we get the wavelength in meters, for example for 80 Hz, the wavelength is 3750 kilometers, for 89 MHz - 3.37 meters, for 2 .4 GHz - 12.5 cm.
The exact formula for calculating the wavelength of electromagnetic radiation in a vacuum is:
where is the speed of light, equal in the International System of Units (SI) to 299,792,458 m/s exactly.
To determine the wavelength of electromagnetic radiation in any medium, use the formula:
where is the refractive index of the medium for radiation with a given frequency.
Notes
Literature
Wikimedia Foundation. 2010.
See what “Wavelength” is in other dictionaries:
The distance between the two closest points of a harmonic wave that are in the same phase. Wavelength λ = vT, where T is the oscillation period, ? phase speed of the wave. * * * WAVELENGTH WAVELENGTH, the distance between the two nearest points... ... encyclopedic Dictionary
wavelength- (λ) The distance by which the surface of an equal phase wave moves during one period of oscillation. [GOST 7601 78] wavelength The distance traveled by an elastic wave in a time equal to one full period of oscillation. )
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