College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
Longitudinal waves are a type of wave in which the displacement of the medium is parallel to the direction of wave propagation. This means the particles in the medium oscillate back and forth in the same direction as the wave is traveling.
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Longitudinal waves transfer energy through the vibration of particles in the medium, rather than the movement of the particles themselves.
Sound waves are a common example of longitudinal waves, as the vibration of air molecules transmits the sound energy.
The speed of longitudinal waves depends on the properties of the medium, such as its density and elasticity.
Longitudinal waves can undergo reflection, refraction, and interference, just like other types of waves.
The Doppler effect, which causes the apparent change in frequency of a wave, applies to longitudinal waves like sound.
Review Questions
Explain how longitudinal waves differ from transverse waves in terms of the motion of the medium.
In longitudinal waves, the particles in the medium oscillate back and forth in the same direction as the wave propagation, whereas in transverse waves, the particles move perpendicular to the direction of wave travel. This means that in longitudinal waves, the displacement of the medium is parallel to the direction of the wave, while in transverse waves, the displacement is perpendicular to the direction of the wave.
Describe the role of compression and rarefaction in the propagation of longitudinal waves.
Compression and rarefaction are key features of longitudinal waves. During compression, the particles in the medium are pushed closer together, resulting in higher pressure. In the rarefaction regions, the particles are pulled farther apart, leading to lower pressure. This alternating pattern of compression and rarefaction is what allows longitudinal waves to transmit energy through the medium, as the pressure changes cause the particles to vibrate and transfer the wave energy.
Analyze how the properties of the medium affect the speed of longitudinal waves, and explain the implications for the Doppler effect.
The speed of longitudinal waves is dependent on the properties of the medium, specifically its density and elasticity. In general, longitudinal waves travel faster in media with higher density and greater elasticity. This relationship between the medium's properties and the wave speed has important implications for the Doppler effect, which describes the apparent change in frequency of a wave due to the relative motion between the source and the observer. The Doppler effect applies to longitudinal waves like sound, and the observed frequency shift is directly related to the speed of the wave in the medium.