# Transverse Waves

## What is a Wave?

While making a journey through the boat to a place like Elephanta caves, we observe that ripples of a sea make vibrations moving the boat forward. These waves move up and down.

This means there is a flow of energy between the particles of a ripple, while it ascends and descends.

The energy flow is in the form of vibrations. So this ascending and descending nature of ripples is like that of waves. We conclude that ripples are waves, and these waves are transverse as they move in the boat’s direction.

We conclude that the transverse waves are the waves in which there is a flow of energy, while the mass remains at its position.

Here, the mass of water remained at rest, while the energy in the form of up and down vibrations led the boat to move forward.

Let’s study transverse waves.

### What Are Transverse Waves?

Transverse waves are the waves in which the vibrations move in a direction perpendicular to that of the direction of propagation of the wave.

A pluck of a string or the ripples of water are examples of transverse waves.

If we observe the waves of water:

Each particle in this wave is executing a simple harmonic motion.

This means particles aren’t moving, they’re just oscillating about their mean position, while the wave moves linearly.

These waves are the up and down vibrations of the ripples of water. We can observe that these waves have symmetry about a centerline.

By symmetrical, I mean, this wave is regular. If we cut a section of a particular crest, then and observe that this section repeats end-to-end to make up the whole wave.

The maximum distance a vibration makes away from the wave centerline (crest or trough)  is the amplitude of the wave.

This is how a transverse wave looks like.

We can consider an example of a light wave to understand what amplitude is.

Let’s take two bulbs of different wattage:

The bulb with 100-W power is brighter. So, we can consider this brightness as an amplitude.

Therefore, Power α (Amplitude)2.

### Sound Waves Are Transverse Waves

If we pluck a string from one end just like this:

The wave is moving ahead with particles moving back and forth, and the direction of motion of particles in a direction perpendicular to the propagation of a wave.

Just like a standing wave in a musical sound. When we play the guitar, it’s string make ripples when we stretch them as shown in the figure below:

We may say that sound waves are transverse. But how can we prove this?

As we took an example of a string. Here, when the wave of particles reaches the end, they invert while coming back. This means when a crest reaches the end while coming back, it turns to a trough as shown in the image below:

We can consider this phenomenon as the reflection of transverse waves.

### Speed of a Transverse Wave

Have a look at the wave of a string:

These waves move from left to right at a constant speed. This speed is the speed of a wave.

### This Speed Depends on Two Factors

1. The wave, and

2. What it is traveling through.

To understand this let’s take transverse waves examples in real life:

1. Waves travel faster in deep water than shallow water.

1. Let’s take two ropes of different widths as shown below:

A thin and a thick rope

Let us generate a pulse (or a wave) in these two ropes:

Wave in a thin rope                           Wave in a thick rope

Now, looking at these two images, we might wonder which wave in which rope would have a greater speed?

Well, the wave would pass with a greater in a thin rope, but how?

Let’s assume, a thin rope as a pipe with a large diameter like this:

The water flow would be fast because the large diameter water pipe would allow the high-flow easily.

Now, let’s assume the thick rope as a water pipe with a smaller diameter:

Now, if the same energy-level water passes through this thin pipe, there will be greater vibrations between the water molecules as they possess higher energy and higher momentum.

From these two examples, we conclude that waves would pass easily through the thick pipe.

We know that the velocity of a transverse wave is:

v = √T/μ.

Where v  = wave speed

T = Tension in the string (N/m), and

μ = linear mass density (mass per unit length (ml) measured in Kg/m.

This velocity is directly proportional to the square root of the tension in a string and inversely proportional to its linear mass density

The speed of a transverse wave decreases with an increase in the mass, but how?

Let’s say I have a light-weighted rope and heavy-weighted rope:

If I pluck these two ropes at one end, the rope with lesser weight would make more waves and travel faster than the heavy-weighted rope.

The speed of the wave increases with an increase in tension, but how?

Let’s take two ropes tied in different ways as shown below:

String tied tightly                                          String tied loosely

In these conditions, if I pluck a string that is tied tightly. It will make larger oscillations than the one which is slackened.

1. What is the Formula for Wave Velocity?

The wave velocity is the speed at which a wave moves with particles makes oscillations about their mean position.

The formula of the wave’s velocity is given by v = fλ

Where f is the wave frequency or the number of waves that pass through a point in a given time.

λ = The distance between two successive crests or troughs in a wave.

2. Why is the Wave Speed Constant?

The speed of the wave is an attribute of the medium.

Changing wave speed requires a change in the medium itself.

So, if the medium in which the wave travels doesn’t change, wave speed remains constant.

3. Does Tension Affect Wave Speed?

Yes, it does!

On increasing the tension in a string, the speed of the wave increases, which in turn, increases the wave frequency, i.e., the number of waves in a given length.

4. What Are Some Properties of a Transverse Wave?

The properties of transverse waves are as follows:

1. The crests and troughs of transverse waves are like peaks of a mountain.

2. Particles move in a direction perpendicular to the direction of propagation of a wave.