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What’s the Difference Between Wave Velocity and Particle Velocity?

What’s the Difference Between Wave Velocity and Particle Velocity?

Waves and particles are two things that are so in sync with one another that we sometimes consider them as one. Take the example of Light, it is sometimes classified as a particle (photons) and sometimes as a wave (Electromagnetic transverse wave).

So you’re wondering if there is any major difference between them, after all a particle moves in sync with the disturbance causing it, i.e the propagation of particle in response to a wave.

The short answer: Absolutely, waves and particles travel at different velocities. Keep in mind that waves are intangible and not physically present.

They are a representation of energy, whereas particles are tangible and physically exist and are made up of matter. Therefore, anything that has mass can not travel at the speed of light, waves are massless and therefore aren’t bound to the same restrictions.

Join me as I thoroughly explain how waves and particles are interconnected yet vastly different from one another.

What’s the Difference Between Wave and Particle?

To understand this question we need to refresh our concepts and understandings of what constitutes a particle and a wave.

A wave is a disturbance in a medium that carries energy without causing net particle movement.  Elastic deformation, a change in pressure, electric or magnetic intensity, electric potential, or temperature, could all be forms of a wave.

Here are the basic properties of any wave:

  • Transfers energy.
  • Usually involves a periodic, repetitive Movement.
  • Does not lead to a net motion of the medium or its particles (mechanical wave).

In this article, we are going to be talking about mechanical waves, i.e Transverse and longitudinal waves.

Here’s a table naming the waves presented to each group.

Types of Transverse Waves and their speedTypes of Longitudinal Waves
Light (300,000,000 m/s)Sound (330 m/s)
Gamma (300,000,000 m/s)Ultra-sound (1540 m/s)
Water ripple (1500 m/s)seismic P-waves (5000 m/s)
The relationship between the velocity of a particle and a wave.

Funnily enough, as of yet, we don’t have a proper concrete definition of what constitutes a particle, and the answers vary depending on who you ask.

Way back in school we learn that matter is made of atoms. And that atoms are made of smaller ingredients: protons, neutrons, and electrons.

The protons and neutrons are of quarks however electrons aren’t. Quarks and electrons, as far as we can tell, are fundamental particles i.e they are not composed of other smaller particles. These are all examples of particles.

However matter larger than these sub-atomic particles also constitute a particle, such as entire molecules and grains of sand or rice. However without digressing particle, for the sake of simplicity let’s classify particles as a small, tangible piece of matter that is affected by waves.

What is Wave Velocity?

Car travelling at changing velocity
A car traveling at a changing velocity.

Wave Velocity is the distance traversed by a periodic motion per unit of time. It normally refers to speed although velocity implies both speed and direction. Also, the velocity of a wave is equal to the product of wavelength and frequency and it’s independent of its intensity.

The definition of velocity is a vector measurement of the rate and direction of motion. Simply say, velocity is the rate at which something moves in a single direction. The speed of a car traveling north on a major freeway and the speed of a rocket launching into space can both be measured using velocity.

Consider speed and velocity the same, except velocity is a vector quantity, i.e it requires both displacement (direction) and magnitude (intensity).

Velocity can simply be defined by the formula, Velocity= Displacement/Time.

So while a person jumping from one side to another side continuously might have a constant speed or accelerating speed, his velocity is 0, as he is not covering any net distance.

How Do Wave Velocity and Particle Velocity Differ From Each Other in Wave Motion?

  1. The velocity with which the wave travels in space is called wave velocity. It is defined as v=frequency∗wavelength.
  2. Particle velocity is the rate at which particles vibrate in order to transfer energy in the form of a wave.
  3. The wave velocity is constant (provided the medium density and frequency of the source are constant), whilst particle velocity varies with time (for a specific particle) or location (for a particular time).

Here’s a thought experiment to help you visualize this concept better.

Consider walking on a platform while juggling a ball in your hand. Examine the ball. The ball moves vertically as a result of your juggling, but it also moves horizontally as you walk on the platform.

The vertical velocity of the ball as a result of juggling is similar to particle velocity, which is the velocity at which a medium particle oscillates around a mean position. While your horizontal velocity on the platform is similar to wave velocity, which is the speed at which the pulse moves through the medium.

They can be correlated using the following equation;

Particle velocity =wave velocity x strain in the medium.

Wave velocity is the velocity with which a wave is propagating or the velocity with which disturbance is moving. But particle velocity is the velocity with which a particle is oscillating. The wave consists of a huge number of oscillating particles.

Therefore, particle velocity is the velocity of an individual particle that is oscillating.

Wave velocity is the overall velocity with which disturbance is moving.

This video should help you understand more clearly.

The relationship between the velocity of a particle and a wave.

Is Particle Velocity Equal to Wave Velocity?

Usually not, but they can be. Particle velocity can either be longitudinal or transverse, aka side to side or up and down. The particles can be moving up and down at the same speed as the propagation, but they can certainly be different.

With longitudinal waves, it’s a bit more interesting since the propagation and particles move in the same direction (if we think of a coordinate plane the particles move forward and back along one axis, and the propagation just moves forward).

This can lead to effects like sonic booms. These effects are called supercritical, which means the particles move faster than the wave propagation.

If they are the same speed it is probably just on the threshold of supercritical, but no different effects. However, frequency does determine resonance.

It usually doesn’t occur at the wave propagation speed, but I’m sure there is a material where it does. Besides resonance, anything not supercritical has similar behavior, so the velocities being equal probably has no additional effects.

Consider a crowd of fans in a stadium doing ‘the wave’. The speed of the wave around the stadium is easily measurable. But none of the ‘particles’ (people) ever leave their seats.

Or consider the speed of a sound wave in the air, 330 or so m/s. Do the moving air particles generate a wind of 330 m/s? No. That would be about 3 times as fast as the fastest wind gust ever recorded on Earth.

So no, the wave velocity will always be larger or in some instances equal to the velocity of a particle in motion due to a wave.

Final Thoughts

Here are the key takeaways from this article:

  • A wave is an intangible form of energy that disturbs matter by interacting with it
  • A particle is a piece of matter and as such is affected by a wave
  • A single wave might affect many particles at any given time, and the velocity of each individual particle could vary from one another. However, the velocity of a wave will always remain constant at all times, granted if the medium is not changed.
  • Waves are energy and as such can travel at the speed of light, particles made up of matter can not.
  • Wave velocity is constant for a given medium while Particle velocity changes with time.
  • Therefore, in most cases, waves would be faster than particles.

I hope this article helps you differentiate between wave and particle velocity.

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