Traveling wave

An electric traveling wave moves on a line from the feed point to the load (terminating resistor). The distance between two neighboring wave crests is the wavelength . ${\displaystyle \lambda }$

A traveling wave is a wave that travels in one direction between parallel boundaries or on a one-dimensionally extended medium (line). The term traveling wave is intended to emphasize the difference to the standing wave and is only common in certain specialist areas.

The traveling wave can be described as an approximately one-dimensional phenomenon with the formula for a plane wave . In the harmonic, d. H. sinusoidal case is the deflection:

${\displaystyle y(x,t)=A\sin(kx-\omega t+\phi )\,}$,

where is the amplitude , the circular wavenumber , the circular frequency , the time and the phase . ${\displaystyle A}$ ${\displaystyle k}$ ${\displaystyle \omega =2\pi f}$ ${\displaystyle t}$ ${\displaystyle \phi }$

The phase velocity of the wave is ${\displaystyle v_{\mathrm {p} }}$

${\displaystyle v_{\mathrm {p} }={\frac {\omega }{k}}=\lambda f}$.

${\displaystyle \lambda }$is the wavelength .

In some areas, the term traveling wave is also used for a single impulse that runs along a line (see e.g. impulse timetable ).

physiology

Cochlea (cochlea), schematic. A: Traveling wave that moves like a rope and leads to displacements in the hair cells; high frequencies at the base and low frequencies at the apex. B: Alternative view showing that hair cells in the neighborhood are also recorded independently.

In physiology, a traveling wave is a wave in the inner ear described by Nobel Prize winner Georg von Békésy . It is created by the entry of sound into the inner ear and deflects the basilar membrane through pressure fluctuations . Depending on its frequency, the wave leads to a maximum deflection at a specific location on the basilar membrane. The relationship between frequency and basilar membrane deflection is given by the mechanical properties of the basilar membrane. The natural frequency of the membrane sections decreases from the base to the tip, corresponding to the decrease in stiffness and the increase in mass. At the point of maximum deflection, the wave ends its migration and is dampened by the antiresonance of the tectorial membrane .

This spatial frequency transformation roughly breaks down the sound signal into its frequencies. Characterized the cochlear amplifier (will cochlear Amplifier ) in the outer hair cells is activated, the extent enhances the decomposition process of the frequencies that certain frequencies can be distinguished from the ear. This mechanism is an important basis for understanding human language.

Electrical engineering and physics

Traveling waves are z. B. in high voltage lines , in electric motors and for power transmission at high frequencies (see waveguides ) observed or used. The signal amplification in traveling wave tubes is based on the coupling of a traveling wave with a focused beam of free-flying electrons. In the traveling wave accelerator , free electrons are brought to high kinetic energy by “surfing” the electromagnetic wave in a suitably shaped waveguide .

If the wave train is spatially limited in the direction of propagation, i.e. if it is an impulse , an envelope can be defined that surrounds it. According to the Fourier analysis, the impulse corresponds to a frequency band whose center of gravity moves with the group speed . If the speed of propagation depends on the wavelength and certain limits are observed, one speaks of dimensionally stable solitons .

See also

• Standing wave ratio
• Ultrasonic motor
• Cochlea

Web links

• Sensory physiology
• Traveling wave in a three-phase machine