por The longitudinal waves They manifest themselves in material media in which the particles oscillate parallel to the direction in which the wave travels. as will be seen in the following images. This is its distinctive feature.
Sound waves, certain waves that appear during an earthquake and those that occur in a slinky or spring when a small impulse is given to it in the same direction as its axis, are good examples of this kind of waves.
Sound is produced when an object (such as the tuning fork in the figure, a musical instrument or simply the vocal cords) is made to vibrate in a medium capable of transmitting the disturbance through the vibration of its molecules. Air is a suitable medium, but so are liquids and solids.
The disturbance repeatedly modifies the pressure and density of the medium. In this way, the wave produces compressions and expansions (rarefactions) in the molecules of the medium, as the energy moves at a certain speed. v.
These changes in pressure are perceived by the ear through vibrations in the eardrum, which the nerve network is responsible for transforming into tiny electrical currents. Upon reaching the brain, it interprets them as sounds.
In a longitudinal wave, the pattern that repeats continuously is called cycleand its duration is period of the wave. In addition there is the amplitudewhich is the maximum intensity and which is measured according to the magnitude that is taken as a reference, in the case of sound it can be the variation of the pressure in the medium.
Another important parameter is the wavelength: the distance between two successive compressions or expansions, see figure 1. In the International System, the wavelength is measured in meters. Finally there is your speed (in meters / second for the International System), which indicates how fast the energy propagates.
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How are longitudinal waves manifested in sea waves?
In an aquatic body, waves are produced by multiple causes (pressure changes, winds, gravitational interactions with other stars). In this way, sea waves can be classified into:
– Wind waves
– Tides
– Tsunamis
The description of these waves is quite complex. In general lines, in deep water the waves move longitudinally, producing periodic compressions and expansions of the medium, as described at the beginning.
However, on the surface of the sea things are a little different, since there the calls predominate. surface waves, which combine characteristics of longitudinal waves and transverse waves. Therefore, the waves that move in the depths of the aquatic environment are very different from those that move on the surface.
A log floating on the sea surface has a sort of swaying movement or a smooth rotation. Indeed, when the waves break on the coast, the longitudinal components of the wave are the ones that predominate, and since the log responds to the movement of the water molecules that surround it, it is also observed coming and going on the surface.
Relationship between depth and wavelength
The factors that determine the type of wave that occurs are: the depth of the water and the wavelength of the sea wave. If the depth of the water at a given point is called dand the wavelength is λ, the waves go from being longitudinal to superficial when:
d < λ/2
At the surface, the water molecules acquire rotational movements that they lose as the depth increases. The friction of the mass of water with the bottom causes these orbits to become elliptical, as shown in figure 2.
On the beaches, the waters near the shore are more restless because the waves break there, the water particles are slowed down at the bottom and this causes more water to accumulate on the crests. In deeper water, on the other hand, it is perceived as the swell softens.
When d >> λ/2 you have deep water waves u short waves, circular or elliptical orbits decrease in size and longitudinal waves predominate. And if d << λ/2 the waves are from surface waters or long waves.
Differences with transverse waves
Both longitudinal and transverse waves fall into the category of mechanical waves, that require a material medium for their propagation.
The major distinction made between the two was mentioned at the beginning: in transverse waves the particles in the medium move perpendicular to the direction of propagation of the wave, while in longitudinal waves they oscillate in the same direction followed by the disturbance. But there are more distinctive features:
More differences between transverse and longitudinal waves
– In a transverse wave, crests and valleys are distinguished, which in longitudinal waves are equivalent to compressions and expansions.
– Another difference is that longitudinal waves are not polarized because the direction of the speed of the wave is the same as that of the movement of the oscillating particles.
– Transverse waves can propagate in any medium and even in a vacuum, like electromagnetic waves. On the other hand, inside the fluids, lacking in rigidity, the particles have no other possibility than to slide against each other and move as the disturbance does, that is, longitudinally.
As a consequence, the waves originated in the middle of the oceanic and atmospheric masses are longitudinal, since the transverse waves require means with sufficient rigidity to allow the characteristic perpendicular movements.
– Longitudinal waves cause pressure and density variations in the medium through which they propagate. On the other hand, transverse waves do not affect the medium in this way.
Similarities Between Longitudinal and Transverse Waves
In common they have the same parts: period, amplitude, frequency, cycles, phase and speed. All waves undergo reflection, refraction, diffraction, interference, and the Doppler shift and carry energy through the medium.
Even though crests and troughs are distinctive of a transverse wave, compressions in the longitudinal wave are analogous to crests and expansions to troughs, so both waves admit the same mathematical description of a sine wave.
Examples of longitudinal waves
Sound waves are the most typical longitudinal waves and are among the most studied, since they are the foundation of communication and musical expression, reasons for their importance in people’s lives. In addition, sound waves have important applications in medicine, both in diagnosis and treatment.
The ultrasound technique for obtaining medical images, as well as for the treatment of kidney stones, among other applications, is well known. Ultrasound is generated by a piezoelectric crystal capable of creating a longitudinal pressure wave when an electric field is applied to it (it also produces a current when pressure is applied).
To really see what a longitudinal wave is like, nothing beats coil springs or slinkys. Giving a small impulse to the spring, it is immediately possible to observe how the compressions and expansions propagate alternately throughout the length of the coils.
– Seismic waves
Longitudinal waves are also part of seismic movements. Earthquakes consist of different kinds of waves, among which are P waves or primaries and S waves or secondaries. The former are longitudinal, while in the latter the particles of the medium vibrate in a transverse direction to the displacement of the wave.
In earthquakes, waves are produced both longitudinal (primary P waves) and transverse (secondary S waves) and of other types, such as Rayleigh waves and Love waves, superficial.
In fact, longitudinal waves are the only ones known to travel through the center of the Earth. Since they only move in liquid or gaseous media, scientists think that the Earth’s core is composed mainly of molten iron.
– Application exercise
P waves and S waves produced during an earthquake travel at different speeds on Earth, so their arrival times at seismograph stations are different (see figure 3). Thanks to this it is possible to determine the distance to the epicenter of the earthquake, through triangulation, using data from three or more stations.
Suppose that vP = 8 km/s is the speed of P waves, while the speed of S waves is vS = 5 km/s. The P waves arrive 2 minutes before the first S waves. How to calculate the distance from the epicenter?
Answer
Let D be the distance between the epicenter and the seismological station. With the data provided, the travel time tP and tS of each wave is found:
vP = D/tP
vS = D/tS
The difference is Δt = tS – tP:
Δt = D/ vS – D/ vP = D (1/ vS – 1/ vP)
Clearing the value of D:
D = Δt / (1/ vS – 1/ vP) =(Δt . vP . vC ) /(vP – vC)
Knowing that 2 minutes = 120 seconds and substituting the rest of the values:
D = 120s. (8 km/s . 5 km/s ) / (8 – 5 km/s) = 1600 km.
References
Difference between Transverse and Longitudinal Waves. Retrieved from: physicsabout.com.
Figueroa, D. 2005. Waves and Quantum Physics. Physics Series for Science and Engineering. Volume 7. Edited by Douglas Figueroa. Simon Bolivar University. 1-58.
Infrasounds and Ultrasounds. Retrieved from: lpi.tel.uva.es
Rex, A. 2011. Fundamentals of Physics. pearson. 263-286.
Russell, D. Longitudinal and Transverse Wave Motion. Retrieved from: acs.psu.edu.
Water Waves. Retrieved from: labman.phys.utk.edu.