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Wave motion is the propagation of disturbances, produced in one part of a medium to the other parts by the vibration of its particles. It is a deviation from a state of rest or equilibrium from place to place in a regular and organized way. Most familiar are surface waves on water, but both sound and light travel as wavelike disturbances, and the motion of all subatomic particles exhibits wavelike properties. The study of waves therefore forms a topic of central importance in all physical science and engineering

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The waves which need a medium for their propagation are Mechanical Waves.
There are mainly two types of mechanical waves.
(1) Transverse Waves
(2) Longitudinal Waves

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A transverse wave is a wave in which the particles of the medium vibrate in a direction perpendicular to the direction of propagation of the wave.

A simple example is given by the waves that can be created on a horizontal length of string by anchoring one end and moving the other end up and down.

Another example is the waves that are created on the membrane of a drum. The waves propagate in directions that are parallel to the membrane plane, but the membrane itself gets displaced up and down, perpendicular to that plane.

Light is another example of a transverse wave, where the oscillations are the electricand magnetic fields, which point at right angles to the ideal light rays that describe the direction of propagation.

Transverse waves commonly occur in elasticsolids; the oscillations in this case are the displacement of the solid particles away from their relaxed position, in directions perpendicular to the propagation of the wave.

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1.Amplitude :
The characteristic height of a peak and depth of a trough is called the amplitude of the wave. The vertical distance between the bottom of the trough and the top of the peak is twice the amplitude. We use symbols agreed upon by convention to label the characteristic quantities of the waves. Normally the letter A is used for the amplitude of a wave. The units of amplitude are metres (m).

2 .Wavelength :
Look a little closer at the peaks and the troughs. The distance between two adjacent (next to each other) peaks is the same no matter which two adjacent peaks you choose. So there is a fixed distance between the peaks.

Looking closer you'll notice that the distance between two adjacent troughs is the same no matter which two troughs you look at. But, more importantly, it is the same as the distance between the peaks. This distance which is a characteristic of the wave is called the wavelength.
Waves have a characteristic wavelength. The units are metres (m).

The wavelength is the distance between any two adjacent points which are in phase. Two points in phase are separate by an integer (0,1,2,3,...) number of complete wave cycles. They don't have to be peaks or trough but they must be separated by a complete number of waves.

3. Period :
The time between two adjacent peaks is same and also the time between two adjacent troughs always the same, no matter which two adjacent troughs you pick. The time you have been measuring is the time for one wavelength to pass by. We call this time the period and it is a characteristic of the wave.

Waves have a characteristic time interval which we call the period of the wave and denote with the symbol T. It is the time it takes for any two adjacent points which are in phase to pass a fixed point. The units are seconds (s).

4 . Frequency :
There is another way of characterising the time interval of a wave. We timed how long it takes for one wavelength to pass a fixed point to get the period. We could also turn this around and say how many waves go by in 1 second.

We can easily determine this number, which we call the frequency and denote f. To determine the frequency, how many waves go per second, we work out what fraction of a waves goes by in 1 second by dividing 1 second by the time it takes T. The unit of frequency is the Hz.
Waves have a characteristic frequency. F=1/T
5 . Speed :
Now if you are watching a wave go by you will notice that they move at a constant velocity. The speed is the distance you travel divided by the time you take to travel that distance. This is excellent because we know that the waves travel a distance equal to wavelength in a time T. This means that we can determine the speed.

There are a number of relationships involving the various characteristic quantities of waves.
A simple example of how this would be useful is how to determine the velocity when you have the frequency and the wavelength. We can take the above equation and substitute the relationship between frequency and period to produce an equation for speed of the form

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A Longitudinal Wave is a wave in which the particles of the medium vibrate in a direction parallel to the direction of propagation of the wave. This creates compressions and rarefactions alternately in the medium.
Longitudinal waves include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an elastic medium) and seismic P-waves (created by earthquakes and explosions). In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization and contrasts with the standing wave along an oscillating guitar string which is transverse.

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DIFFERENCE BETWEEN TRANSVERSE AND LONGITUDINAL WAVES

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DIFFERENCE BETWEEN TRANSVERSE AND LONGITUDINAL WAVES

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https://www.bbc.co.uk/bitesize/guides/z9bw6yc/test