Longitudinal wave

A longitudinal wave - also called longitudinal wave - is a physical wave that oscillates in the propagation direction. Its counterpart is the transverse wave whose amplitude is perpendicular to the propagation direction. The standard example for longitudinal waves is sound in gases or liquids.

Wavelength and speed

The wavelength (Greek lambda) is the distance between two adjacent same vibrational states, eg two wave crests. Is the excitation frequency f = 1 / T is increased, the wavelength becomes smaller. If the wave velocity ( velocity of propagation of the wave in the medium) increases, the wavelength is larger. Therefore, results for the wavelength of the following equation:

Where c is the propagation speed of the wave ( ' phase speed ' ), and f is the frequency.

Is different from the phase velocity of the so-called " group velocity ", which in the superposition ( superposition ) occurs by wave trains or shaft groups and in particular describes the speed of the transport of energy. During the phase velocity can be written as, with the angular frequency and wave number of the circle, applies to the group velocity, with the differential symbols.

Phase and group velocity are different in general, except for the absence of non-linear terms in the amplitudes. It can be shown that the group velocity can never be greater in contrast to the phase velocity than the velocity of light in vacuum.

Propagation principle

Longitudinal waves are pressure waves. This means that in a medium zones of increased pressure or compressive stress to propagate (or negative pressure or tension ) in the propagation direction or to move or spread.

The individual particles in the dispersion medium, atoms or molecules that vibrate in this direction of propagation, by the amount of the amplitude of back and forth. After the passage of vibration to the particles to move back to its rest position, the position of equilibrium to return. By the propagation of the vibration energy is not lost, with the exception of friction losses between the particles.

• In an elongated body ( spring, tape, rod, wire ) the amount of amplitude at all points of the medium is the same.
• On propagation of a concentrated source in the space, the power density decreases with the square of the distance from the source, as the area enclosed by the angled surface increases quadratically with the distance.

The power of a longitudinal wave is proportional to the square of the amplitude of the deflection of the pressure or tension; see also sound pressure and particle velocity.

Examples

Mechanical longitudinal waves can be in any medium, whether solid, liquid or gaseous spread, whereas mechanical transverse waves can propagate only in solids themselves.

A typical example of a longitudinal wave is sound, which can occur in gases and liquids as longitudinal waves only.

Comparisons and characteristics

Have longitudinal waves in the same solid medium, a higher speed than the transverse waves of the same type with otherwise identical parameters.

Longitudinal seismic waves are called P- waves. Always take a first and have a lower potential for destruction during earthquakes as shear waves. In contrast, the ( longitudinal ) water waves, " tsunamis " cause.

In plasmas and in other electrical conductors, there are electromagnetic longitudinal waves in addition to the electromagnetic transverse waves.