 # Travelling Wave

Have you ever sat by a lake and observed the waves created on the surface of the water when you throw a stone into it? This is a good visual example of the propagation of waves and makes it simpler for you to understand travelling of waves and all other concepts related to it. Our universe has an amazing way of informing us about any changes in the physical world. When there are changes the information about that disturbance moves gradually outwards. It moves far from the source of disturbance in all the directions. When the said information travels, it travels in the form of a wave, just like the way waves are created when you throw a stone in the still water. This is known as the travelling wave.

### Define Travelling Wave

Before understanding what is travelling wave, let’s understand waves. Wave can be defined as a disturbance in a medium that travels transferring momentum and energy without any actual movement of the medium. However, the medium must have elastic properties. In our everyday life, there are many examples of waves, for example, ocean waves, strings of musical instruments, etc. On the other hand, a travelling wave is a wave in which the positions of minimum and maximum amplitude travel through the medium.

### Points To Remember

Here are some of the points that are necessary to keep in mind about the wave:

• Every wave has a high point and a low point. The high points are known by the name of crests. On the other hand, the low points are named by troughs.

• Amplitude is the maximum distance of the disturbance from the midpoint of the wave to either the top of the crest or the bottom of a trough.

• The maximum distance between the two adjacent troughs or the two adjacent crests is known as a wavelength.

• Now, the time period is actually the time taken to complete one vibration.

• Frequency is the number of vibrations the wave undergoes in one second.

• You can witness an inverse relationship between both frequency and time period. The relationship is given below,

T=1f

• The speed of a wave is given by the travelling wave equation,

V=λf

Where 𝛌 is the wavelength.

### What are the Various Types of Travelling Waves?

Each type of wave contains different characteristics. And with these characteristics, we can easily distinguish between them. Here is a list of different types of waves that have been categorized based upon their particle motion.

Pulse Waves - the sudden disturbance that travels through a medium is known as a pulse wave. The disturbance can be caused by a chain reaction or sudden compression of air caused by an explosion. One example of a pulse wave is thunder. It comprises only one crest that travels through the transmission medium.

Continuous Waves - it is an electromagnetic wave that has constant amplitude and frequency. It is a typical sine wave and is considered to be of infinite duration. It was used in the earlier days of radio transmission.

Transverse Waves - in the transverse wave, the movement of the particles is at right angles to the motion of the energy. It is generated through a solid object like a stretched rope. Trampoline is the best example to understand this wave.

Longitudinal Waves - in this type of travelling wave the motion of the wave-particle is in the same direction as the propagation of the wave. In simple words, the movement of the particles is parallel to the motion of the energy. The best example for longitudinal waves is sound waves moving through the air when you hear a loudspeaker playing in the distance.

There is a second way to characterize the waves by types of matter they are able to move or travel through.

• Electromagnetic Waves - this type of wave can travel easily through a vacuum. It does not need any medium, soft or hard to travel. An example of an electromagnetic wave is mobile phone waves or sound waves. They don't need any vacuum to travel.

• Physical waves - Unlike electromagnetic waves, they require a medium to travel. They are further distinguished on the basis of phases of matter through which they can move.

• Longitudinal Waves - these waves can easily pass through liquids and games.

• Transverse Waves - they require a solid material or medium to propagate.

Problems based on travelling wave equation

### Solved Examples

1: A wave on a rope is shown on the right at some time t.  What is the wavelength of this wave?  If the said frequency is about 4 Hz, what will be the wave speed?

Solution:

Now, for all the periodic waves, you will find v = λ/T = λf.

Details of the calculation:

The wavelength λ is 3 m. The speed is v = λf = (3 m)(4/s) = 12 m/s.