Transverse and longitudinal waves are different types of mechanical waves. A wave can be defined as a dynamic disturbance travelling from one point of medium to another, it is further associated with one or more medium properties. Waves based on their propagation, production, dimension, etc., can be classified into various categories like matter waves, standing waves, progressive waves, gravitational, etc. Out of all these, the most familiar waves, such as waves on a string, water waves, sound waves, etc., are referred to as mechanical waves.

Transverse Waves

The type of mechanical wave in which the oscillation of the constituents of the medium is perpendicular to the direction of propagation of the wave, such wave is called a transverse wave. In these waves, particles are displaced at right angles to the wave direction.

Basically, we can say Transverse waves will have oscillations perpendicular to the direction of travel as shown in Figure below.

To visualise how a transverse wave travels through a medium, consider the following scenario: 

Take a long rope and stick it to a wall. Hold the rope at its free end and stretch the rope such that it is taut. Now carefully give a single jerk (up and down movement) to the rope. You will see that a small pulse is created in the rope that travels away from you. The figure below shows this phenomenon. 

Observation:

1. As the wave moves along the rope, each constituent atom of the rope shifts up and down from its mean position generating a series of crests and troughs.
2. You will observe that all rope points get displaced momentarily as this pulse or disturbance travels through them, but as soon as the disturbance moves away, they come to rest.
3. If the rope is very long compared to the size of the pulse, the pulse will die out before reaching the wall. But if the length of the rope and size of the pulse is appropriate enough, we will be able to see the pulse getting reflected after it strikes the wall.
4. Now instead of a single jerk, if you shake the rope sinusoidally up and down continuously, you will find that a periodic sinusoidal disturbance is created on the rope, and the elements of the rope oscillate about their equilibrium mean position as the pulse or wave passes through them.
5.  These oscillations are normal to the direction of motion of the wave along the rope.  This is an example of a transverse wave.

Notes:

1. Crest: Crest is the point on a wave, where the value of upward displacement is maximum, i.e. the highest point on a wave.
2. Trough: Trough is a point on a wave, where the value of downward displacement is maximum, i.e. the lowest point on a wave.

Some Examples of Transverse Waves

1. The ripples observed on the surface of the water.
2. The vibrations produced on a guitar string when it is plucked.
3. The seismic secondary waves or S−$�-$waves during an earthquake.
4. Light waves, radio waves, and other electromagnetic waves.

Longitudinal wave

Longitudinal waves are waves where the displacement of the medium is in the same direction as the direction of the travelling wave. 

The distance between the centres of two consecutive regions of compression or the rarefaction is defined by wavelength, \(\lambda\). When the compression and rarefaction regions of two waves coincide with each other, it is known as constructive interference and if the regions of compression and rarefaction do not coincide, it is known as destructive interference. This is shown in the figure below.

Compression in a longitudinal wave is a region where the particles are the closest together while rarefaction in a longitudinal wave is a region where the particles are spread out.

To visualise how a longitudinal wave travels through a medium, consider the following scenario as shown below:

1. We have all been vaccinated to prevent us from getting affected by a disease. The vaccine dose is put in our body by a syringe. The motion of the piston in a syringe can produce longitudinal waves.
2. Take a long syringe, i.e. a long pipe with a piston at one end. Now push the piston of the syringe up and slowly pull the syringe down such that the injection tube is now filled with air.
3. Give a single push forward and a simultaneous pull back to the piston. You will find with the push, a high-density region and with the pull, a low-density region is created.
4. This pulse so created travels along the length of the injection tube containing compression followed by rarefaction.
5. Suppose this push and pull of the piston is sinusoidal and continuous. In that case, a sinusoidal wave is generated in the air around the injection, which travels along the length of the injection tube.
6. The oscillations of the elements of air in the syringe are along the direction of wave motion. Thus a longitudinal wave is created.

Note:

1. Compression: Compressions are the region of high pressure formed when particles of the medium are very close.
2. Rarefaction: Rarefactions are the region of low pressure formed when particles of the medium are far apart.

Some Examples of Longitudinal Waves

1. The sound waves produced as we talk.
2. The ultrasound waves.
3. The seismic pressure waves or P−$�-$waves associated with Earthquakes.

Example 15.1: Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both:
(a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
(b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.
(c) Waves produced by a motorboat sailing in water.
(d) Ultrasonic waves in air produced by a vibrating quartz crystal.

Solution:

(a) Transverse and longitudinal
(b) Longitudinal
(c) Transverse and longitudinal
(d) Longitudinal