# What is relation between particle velocity and wave velocity?

Table of Contents

- 1 What is relation between particle velocity and wave velocity?
- 2 Is wave velocity is equal to particle velocity?
- 3 What is the angle between particle velocity and wave velocity in transverse wave?
- 4 What is de Broglie equation?
- 5 Is particle velocity greater than wave velocity?
- 6 How do you derive a wave equation?
- 7 What is the difference between wave and particle velocity?
- 8 How do you calculate the particle displacement of sound waves?

## What is relation between particle velocity and wave velocity?

i.e., Particle velocity = – wave velocity × strain. Particle velocity changes with the time but the wave velocity is constant in a medium.

## Is wave velocity is equal to particle velocity?

Particle velocity is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s)….Particle velocity.

Sound measurements | |
---|---|

Sound pressure | p, SPL,LPA |

Particle velocity | v, SVL |

Particle displacement | δ |

Sound intensity | I, SIL |

**How do wave velocity and particle velocity differ from each other?**

The wave velocity remains constant (provided the density of medium and frequency of source is constant), whereas particle velocity depends on the time (for a particular particle) or depends on where the particle is (for a particular time).

**How do you find the velocity of a particle in a wave?**

The wave moves with a constant velocity vw , where the particles of the medium oscillate about an equilibrium position. The constant velocity of a wave can be found by v=λT=ωk. v = λ T = ω k .

### What is the angle between particle velocity and wave velocity in transverse wave?

As already mentioned, in transverse waves the particles of the medium are vibrating at right angles to the direction in which the wave is propagating. This is known as direction of wave velocity. So the angle between the particle velocity and wave velocity in the given transverse wave will be $\dfrac{\pi }{2}$.

### What is de Broglie equation?

The de Broglie equation is an equation used to describe the wave properties of matter, specifically, the wave nature of the electron: λ = h/mv, where λ is wavelength, h is Planck’s constant, m is the mass of a particle, moving at a velocity v. de Broglie suggested that particles can exhibit properties of waves.

**Is wave velocity greater than particle velocity?**

De Broglie concluded that velocity of the particle should always be equal the group velocity of the corresponding wave. As such magnitude of the group velocity is equal to the particle’s speed.

**What is the phase difference between the particle velocity and wave velocity in a transverse wave?**

The angle between particle velocity and wave velocity in transverse wave is. π rad.

## Is particle velocity greater than wave velocity?

According to theory of special relativity, speed of particle vthe phase velocity of matter waves always exceeds c .

## How do you derive a wave equation?

The wave equation is derived by applying F=ma to an infinitesimal length dx of string (see the diagram below). We picture our little length of string as bobbing up and down in simple harmonic motion, which we can verify by finding the net force on it as follows.

**What is the equation of the velocity of this particle?**

The velocity of a particle moving along the x-axis varies with time according to v(t)=A+Bt−1 v ( t ) = A + B t − 1 , where A = 2 m/s, B = 0.25 m, and 1.0s≤t≤8.0s 1.0 s ≤ t ≤ 8.0 s .

**What is the angle produced in case of transverse wave with the direction of propagation?**

Transverse waves occur when a disturbance causes oscillations perpendicular (at right angles) to the propagation (the direction of energy transfer).

### What is the difference between wave and particle velocity?

Wave velocity is the velocity with which progressive wave front travels forward. It is constant throughout the media if the media is homogenous and given by, v = v λ. Particle velocity is the velocity with which particles vibrate during the wave propagation.

### How do you calculate the particle displacement of sound waves?

The particle displacement can be written as u=Aexp (x/a- t) where a is wave velocity, A is amplitude, x is distance and t is time. When sound waves travel, the medium that is air gets strained. The strain is given by du/dx which comes out to be (A/a) exp (x/a- t).

**What is the relationship between phase velocity and group velocity?**

The velocity at which the group, or packet, or particle, propagates is the group velocity. It should be noted that phase and group velocity are not independent. They satisfy the relation v_phase*v_group = c^2, where c is the speed of light.

**Why is the momentum of a particle different for each particle?**

As momentum of every particle is different because momentum p= mv which means that the mass and the velocity of particle is different for different particle. Means as wavelength changes the velocity also changes. Because mass and Planck constant remains constant for the particular particle of the matter.