Progressive Wave

Dhristi JEE 2022-24

Introduction to Progressive Wave

A wave that generally travels continuously in a medium of the same direction without the change in its amplitude is known as a traveling wave or a progressive wave.

 

Let us consider the example of a progressive wave on a string. Here, we will describe the relationship.  

 

In the subjects of Maths and Physics, we will see that this topic is very much related. A propagating dynamic disturbance is known as the waves of one or even more than one quantity. We will discover further about the waves and its progressiveness in this article.

 

What is Progressive Wave

An equation generally can be formed to represent generally the displacement of a particle that is vibrating in a medium through which a wave passes. Thus, we can see that each particle of a progressive wave executes simple harmonic motion of the same period and amplitude differing in phase from each other.

 

Let us now assume that a wave that is progressive generally travels from the origin O along the positive direction of the X-axis from left to right. The displacement of a particle at a given instant is as follows: 

 

y = a sin ωt            …... (1)

 

where we can see that a is the amplitude of the vibration of the particle and then ω = 2πn.

 

The displacement of the particle denoted by letter P at a distance x from O at a given instant is given by,

 

y = a sin (ωt - φ)           …... (2)

 

If two particles are said to be separated by a distance by symbol λ they will differ by a phase of 2π. Therefore we can say that the phase denoted by symbol φ of the particle P at a distance

 

x is  φ = 2π/λ x

 

y = a sin *ωt - 2πx/λ          …... (3)

 

Since we see that the symbol ω = 2πn = 2π (v/λ), the equation is given by

 

y = a sin

 

(2πvt/λ)−(2πx/λ)

 

(2πvt/λ)−(2πx/λ) 

 

y =  a sin 2π/λ (vt – x)               …... (4)

 

Since ω = 2π/T we see that the equation (3) can also be written as,

 

y = a sin 2π *t/T – x/λ)            …... (5)

 

If the wave that generally travels in the direction which is opposite the equation generally becomes

 

y = a sin 2π (t/T + x/λ)             …... (6)

 

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Progressive Wave - Important Points

  • Each particle that is present in the medium executes the vibration which is about its mean position. The disturbance that progresses is from one particle to another.

  • The particles of the medium vibrate with the same amplitude about their mean positions.

  • Each particle or we can say that the successive particle of the medium performs a motion similar to that of its predecessor along the direction of the propagation of the wave, but later in time.

  • The phase of every particle changes from 0 to 2π.

  • No particle generally remains permanently at the position which is at rest. Twice during each vibration, the particles are momentarily at rest at extreme positions. The particles which are different attain the position at different times.

  • The transverse progression of the waves is characterized by crests and troughs. The waves which are longitudinal are characterized by compressions and rarefactions.

  • There is an energy transfer as well which is across the medium in the direction of propagation of progressive waves.

  • All the particles generally have the same maximum velocity when they pass through the mean position.

  • The displacement of the velocity and acceleration as well of the particle separated by the equation that is mλ are the same, where m is an integer. 

 

The Intensity of Progressive Wave

If we generally hear the sound which is produced by violin and the instrument flute or harmonium, we get a pleasing sensation in the ear whereas the sound which is produced by a gun, horn, a motor car, etc., generally produces unpleasant sensation in the ear.

 

The loudness that is generated by the sound depends on the intensity of the sound wave and the sensitivity of the ear.

 

The intensity is generally defined as the amount of energy that is crossing per unit area per unit time that is perpendicular to the direction with respect to the propagation of the wave.

 

Intensity is measured in the W m–2.

 

Types of Progressive waves 

Progressive waves are also known as traveling waves. It reveals continuously. The main characteristic of a progressive wave is that it travels in continuity without a stop or change in its amplitude or direction. If there is one or even more than one quantity, then it is known as a propagating dynamic disturbance.

 

Progressive waves are further classified into two types. One: transverse wave and the second: longitudinal beam. To see how transverse waves are formed, first take a long rope and attach one end to a peg on a wall, stretch it and set it to oscillate up and down at the free end. A bump is formed on the rope which travels in the forward direction. These waves are called transverse waves. 

 

Here, in a transverse progressive wave, the displacement of particles of a medium are at right angles to the direction of the propagation of the wave. When a stone is dropped and still, the water surrounding it moves up and down, therefore right causing circular peaks a circular depression is formed around its circular peak. Thus alternate peaks and depressions are formed with an increasing radius; the peaks are called crest and the depressions are called trough. A crest and a trough make up a wave. 

 

A longitudinal wave is another type of progressive wave. When the displacement of particles of the medium is parallel to the direction of propagation of the wave, the wave is said to be a longitudinal progressive wave. When a spring-mass system oscillates, a longitudinal progressive wave travels along its length in the form of compression and rarefaction. 

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FAQs (Frequently Asked Questions)

1. What is a progressive wave and a stationary wave?

Stationary waves and progressive waves are the two categories in which the waves are said to be classified. In a stationary wave, no significant energy transfer is noticed as the energy is confined within the medium. On the contrary, we can say that in progressive waves energy that is said to be transferred among the molecules to reach a specific position.

2. What are the three types of progressive waves?

We can compare and contrast the properties of the three types of progressive waves that are the longitudinal and transverse and orbital waves. The wave which is the transverse: the particles generally move back and forth at right angles to the direction of energy transmission.

3. What are the characteristics of progressive waves?

Characteristics which is of that are progressive are:

  • Each particle of the medium generally executes vibration about its mean position.

  • The particles of the medium vibrate with the same amplitude about their mean positions.

  • Each successive particle of the medium performs a motion similar to that of its predecessor along the direction of propagation of the wave but later in time.

4. Explain how a progressive wave is different from a standing wave?

The standing waves generally consist of nodes and antinodes whereas the progressive wave consists of crests and trough. The stationary waves are produced by the intersection of opposite waves but the progressive waves are formed by any disturbance in the medium.

5. What is the best method to study progressive waves?

The best method to study progressive waves is to freshen up and master the basics regarding the topic. To get hold of the basics, it is important to drill the core concepts because when the core concepts are understood and memorized, the theories that come later can be easily comprehended and mastered. The formulas and theories that are the fundamentals in the topic should be thoroughly apprehended. Students are advised to refer to the resource materials provided by Vedantu for specific learning about progressive waves. 

6. What are the main points to remember about progressive waves?

Some waves are produced and the vibrations travel in all directions through the air around the source. If the waves on their way do not encounter obstacles like a wall or some other object, they continue to travel in the medium without interruption. An example of progressive waves is when a stone is dropped into a pond of water, waves travel from the point of disturbance till they reach the shore such water waves. Another example of progressive is bell ringing. When it rings and vibrates, the waves never return. 

7. How is progressive wave explained easily?

This means the sound waves propagate through the air indefinitely till the energy carried by them becomes zero because of damping, such waves are called progressive waves. They do not return to the source at all so we can define the progressive wave as a wave that travels from a point into an infinite medium and never returns to the origin. The progressive wave’s amplitude is the same for all particles. 


The progressive wave frequency is the same for all particles. 

8. What is an example of a longitudinal wave, of the progressive wave?

In a tube filled with a liquid, if we push the piston forward, the liquid in front of it is compressed. This compressed liquid moves forward, compressing the liquid lays next to it and the compressional pulse travels down the tube. By withdrawing the piston, we allow the liquid in front of it to expand, and a pulse of rarefaction travels down the tube. If the piston oscillates back and forth, a continuous strain of compressions and rarefactions will travel along the tube. Since the oscillating liquid particles are displaced along the direction of propagation, these pulses are called longitudinal waves. Some waves are longitudinal waves that travel through solids, liquids and gasses.

9. What are the fundamental points in progressive waves?

  • Energy and information are transferred through wave motion. This does not include matter. 

  • The vibrating source is the reason waves are caused.

  • An oscillation or a vibration that transfers energy and information are called nothing but a progressive wave.

  • That only has transportation of energy, disturbing the substance which the wave moves.

  • There is an oscillation in the fixed position of the particles in the substance but they do not change or move places.

  • The frequency that is measured in hertz is the number of wave cycles that occur per second.

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