A longitudinal periodic wave is a wave in which the particles of the medium oscillate parallel to the direction of propagation of the wave. Regions of compression and rarefaction are formed where the wave goes through the medium. These waves repeat themselves at regular intervals, hence they are called periodic waves. Longitudinal periodic waves are very important for sound waves, seismic waves, and other phenomena of this nature. This is an important topic for MDCAT students while solving physics problems involving wave motion and energy flow.
Characteristics
Particle Motion: In a longitudinal wave, the particles constituting the wave move back and forth parallel to the direction the wave travels. Thus, it results in regions of compression and rarefaction, or particles tightly packed in compressions and widely spaced in rarefactions. The back-and-forth motion transfers energy in such media.
Compressions and Rarefactions
Compression: That region of the wave, where particles are closely packed, yielding higher pressure.
Rarefaction: A region of the wave where particles are spread apart, leading to lower pressure.
Amplitude: The amplitude of a longitudinal wave refers to the maximum displacement of particles from their equilibrium position during oscillation. For longitudinal waves, amplitude is related to the density of compressions and rarefactions—the greater the amplitude, the more pronounced these regions are.
Wavelength: The wavelength (
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λ) of a longitudinal wave is the distance between two consecutive compressions (or rarefactions) along the wave. This is the repeating unit of the wave’s structure, and it helps in determining the wave’s frequency and speed.
Frequency and Time Period: The frequency (
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f) of a longitudinal periodic wave is the number of cycles that pass a given point per second. The time period (
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T) is the time it takes for one complete cycle to occur. These are inversely related:
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=
1
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f=
T
1
andT=
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1
Wave Speed: The wave speed (
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v) of a longitudinal wave is determined by the medium through which it travels. The speed of sound, for instance, is a longitudinal wave that has different speeds in solids, liquids, and gases. The relationship between wave speed (????v), frequency (????f), and wavelength (????λ) is given by:
????=????????v=fλ
Examples of Longitudinal Periodic Waves
Sound Waves: Sound is a classic example of a longitudinal periodic wave. In sound waves, particles in a medium such as air oscillate back and forth, creating regions of compression and rarefaction that propagate through the medium. Sound requires a medium to travel, and its speed varies depending on the density and elasticity of the medium.
Seismic Waves: Some seismic waves, such as P-waves (primary waves), are longitudinal waves that travel through the Earth’s interior. These waves cause particles in the Earth’s crust to move in the direction of wave propagation, creating regions of compression and rarefaction. P-waves are faster than other types of seismic waves and can travel through both solids and liquids.
Pressure Waves in Fluids: Longitudinal waves also occur in fluids, where pressure waves move through liquids and gases. These waves transfer energy through compressions and rarefactions, similar to sound waves, and they are often observed in the movement of fluids in pipes or during water sloshing in a tank.
Mathematical Representation of Longitudinal Periodic Waves
The displacement of particles in a longitudinal periodic wave can be expressed mathematically using a sinusoidal function similar to transverse waves. For a sinusoidal longitudinal wave, the displacement ????(????,????)y(x,t) at position ????x and time ????t is given by:
????(????,????)=????sin(????????−????????) y(x,t)=Asin(kx−ωt)
where:
????(????,????)y(x,t) is the displacement of a particle at position ????x and time ????t,
????A is the amplitude,
????k is the wave number,
????ω is the angular frequency,
????x is the position, and
????t is the time.
This equation models the oscillation of particles in the medium as the longitudinal wave propagates through it, where ????(????,????)y(x,t) represents the variation of particle displacement with respect to time and position.
Wave Behavior and Energy Transfer in Longitudinal Periodic Waves
Longitudinal periodic waves transfer energy through the medium in the form of pressure variations. The energy of the wave is associated with its amplitude and frequency, and this energy is transferred by the repeated oscillations of particles.
Energy Transfer: In longitudinal waves, energy is transferred through the medium via the oscillation of particles. As particles compress and rarefy, they pass the energy on to adjacent particles, allowing the wave to propagate through the medium. The larger the amplitude, the more energy is transferred.
Reflection and Refraction: When longitudinal waves encounter boundaries, such as the surface of the Earth or the walls of a container, they can be reflected back into the medium. Refraction can occur when the wave passes from one medium into another (for example, from air to water), causing changes in wave speed and wavelength.
MDCAT Quiz: Longitudinal Periodic Waves Questions
Understanding longitudinal periodic waves enables MDCAT students to answer questions related to sound waves, seismic waves, and other types of mechanical waves. In the MDCAT Quiz, students may be asked to calculate wave speed, frequency, or wavelength or analyze the behavior of longitudinal waves in different media. Application of concepts like amplitude, compression, rarefaction, and wave speed is a must for takers to succeed in the physics sections of this exam.
Free Flashcards for Longitudinal Periodic Waves
Free flashcards on longitudinal periodic waves will enable MDCAT students to ace the main ideas related to these waves. Such flashcards may contain diagrams of compressions and rarefactions, explain wave properties such as amplitude and wavelength, or even contain sample problems to practice the wave equation. The regular use of flashcards will strengthen the understanding of longitudinal waves and improve performance in the MDCAT Quiz.
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