LONGITUDINAL WAVES: CHARACTERISTICS, DIFFERENCES, EXAMPLES - PHYSICAL - 2025

The longitudinal waves are manifested in material means in which particles oscillate parallel to the direction 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 are produced in a slinky or spring when it is given a small impulse in the same direction of its axis, are good examples of this class of waves.

Figure 1. Sound is a longitudinal wave that produces successive compressions and expansions in the air. Source: Wikimedia Commons. Pluke

Sound is produced when an object (such as the figure's tuning fork, 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 also liquids and solids are.

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 a cycle, and its duration is the period of the wave. There is also the amplitude, which 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 its speed (in meters / second for the International System), which indicates how fast the energy propagates.

How do longitudinal waves appear in ocean waves?

In an aquatic body, waves are produced by multiple causes (pressure changes, winds, gravitational interactions with other stars). In this way, marine waves can be classified into:

- Wind waves

- Tides

- Tsunamis

The description of these waves is quite complex. In general lines, in deep waters 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 so-called surface waves predominate, which combine characteristics of longitudinal waves and transverse waves. Therefore, the waves that move in the depths of the aquatic environment differ greatly from those that move on the surface.

A log floating on the sea surface has a kind of reciprocating or gently rotating movement. Indeed, when the waves break on the shore, it is the longitudinal components of the wave that predominate, and as the log responds to the movement of the water molecules that surround it, it is also observed coming and going on the surface.

Figure 2. Sea waves on the surface are waves that partly have longitudinal wave characteristics and partly transverse. Source: Source: Vargklo at en.wikipedia

Relationship between depth and wavelength

The factors that determine the type of wave that is produced 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 d, and the wavelength is λ, the waves go from being longitudinal to superficial when:

On the surface, the water molecules acquire rotational movements that they lose as the depth increases. The friction of the water mass 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 ridges. In deeper waters, on the other hand, it is perceived how the waves soften.

When d >> λ / 2 we have deep-water waves or 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 shear waves

Both longitudinal and transverse waves fall into the category of mechanical waves, which require a material medium for their propagation.

The major distinction made between the two was mentioned at the beginning: in transverse waves the particles of 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 ones 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.

- The transverse waves can propagate in any medium and even in a vacuum, such as electromagnetic waves. On the other hand, inside fluids, lacking rigidity, the particles have no choice but to slide past each other and move as the disturbance does, that is, longitudinally.

As a consequence, the waves originating in the middle of oceanic and atmospheric masses are longitudinal, since transverse waves require media 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, the transverse waves do not affect the medium in this way.

Similarities Between Longitudinal and Transverse Waves

They have the same parts in common: period, amplitude, frequency, cycles, phase, and speed. All waves undergo reflection, refraction, diffraction, interference, and the Doppler effect and carry energy through the medium.

Even though the peaks and valleys are distinctive of a transverse wave, the compressions in the longitudinal wave are analogous to the peaks and the expansions to the valleys, in such a way that both waves admit the same mathematical description of sine or sinusoidal 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 in treatment.

The ultrasound technique is well known for obtaining medical images, as well as for the treatment of kidney stones, among other applications. 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 it).

To really see what a longitudinal wave looks like, nothing better than coil springs or slinkys. By giving a small impulse to the spring, it is immediate to observe how the compressions and expansions are propagated alternately throughout the turns.

- Seismic waves

Longitudinal waves are also part of seismic movements. Earthquakes consist of different kinds of waves, among which are P or primary waves and S or secondary waves. The former are longitudinal, while in the latter the medium particles vibrate in a direction transverse to the displacement of the wave.

In earthquakes, both longitudinal waves (primary P waves) and transverse waves (secondary S waves) and other types, such as Rayleigh waves and Love waves, surface.

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 seismographic stations are different (see figure 3). Thanks to this, it is possible to determine the distance to the epicenter of the earthquake, by triangulation, using data from three or more stations.

Figure 3. The seismic waves P and S arrive at the seismographs with different times, since their speeds are different. Source: Wikimedia Commons.

Suppose that v _P = 8 km / s is the speed of the P waves, while the speed of the S waves is v _S = 5 km / s. The P waves arrive 2 minutes before the first S waves. How to calculate the distance from the epicenter?

Reply

Let D be the distance between the epicenter and the seismological station. With the data supplied, the travel time t _P and t _S of each wave can be found:

v _P = D / t _P

v _S = D / t _S

The difference is Δt = t _S - t _P:

Δt = D / v _S - D / v _P = D (1 / v _S - 1 / v _P)

Solving for the value of D:

D = Δt / (1 / v _S - 1 / v _P) = (Δt. V _P. V _C) / (v _P - v _C)

Knowing that 2 minutes = 120 seconds and substituting the rest of the values:

D = 120 s. (8 km / s. 5 km / s) / (8 - 5 km / s) = 1600 km.

References

1. Difference between Transverse and Longitudinal Waves. Recovered from: physicsabout.com.
2. Figueroa, D. 2005. Waves and Quantum Physics. Physics Series for Science and Engineering. Volume 7. Edited by Douglas Figueroa. Simon Bolivar University. 1-58.
3. Infrasound and Ultrasound. Recovered from: lpi.tel.uva.es
4. Rex, A. 2011. Fundamentals of Physics. Pearson. 263-286.
5. Russell, D. Longitudinal and Transverse Wave Motion. Retrieved from: acs.psu.edu.
6. Water Waves. Retrieved from: labman.phys.utk.edu.