Mechanical Waves- Waves and their applications - science lessons for life

## Friday, December 9, 2016

Waves and their Applications
You have seen the ripples formed when you drop a pebble onto a still water surface. The disturbance caused by the pebble spreads over the water surface in the form of circles centered around the point where the pebble hit the water surface as shown below Figure
Formation of ripples on a water surface.

If you hold a rope horizontally as shown below Figure, and then shake the rope up and down, you will observe ripples forming in the rope. Here too the disturbance caused by the hand travels along the rope.
Formation of ripples on a horizontal string
Such a disturbance propagating through a medium or space is known as a wave. If you place an object like a plastic ball on the water surface and then disturb the water surface, how would the plastic ball move?
You will observe that the plastic ball moves up and down perpendicular to the water surface. In order for the ball to move up and down, energy must be transmitted to the ball. Here, energy was transmitted to the ball through the water waves.
An important property of waves is that they carry energy from one point to another. This energy transmission takes place in a manner that does not transmit the substance of the medium between the points concerned.

As an example, when a water wave travels on a water surface, although the water particles at each point move up and down, the water particles do not travel along with the water wave.

Wave Motion
In the two examples given above, the waves propagate through a certain medium. The medium in the case of water waves is water. The medium in the case of waves propagating along the rope is the material of the rope. The motion of the particles in each medium transmits energy in the form of waves through the medium even though the particles themselves do not travel along with the wave. Apart from the two media mentioned above, waves propagate through many other media.

We hear various sounds through sound waves propagating through air. Sound propagates not only through air but also through liquids and solids.

In addition to waves that travel through various media, there are waves traveling without a material medium. Light is an example for a wave that travels without a medium. Although there are regions between the sun and the earth without any material medium, the earth receives light and heat from the sun. Light and heat from the sun arrive at the earth as electromagnetic waves and a material medium is not required for the propagation of electromagnetic waves.

Radio waves too are a form of electromagnetic waves. Radio programs transmitted by a radio transmission station reach the radio set in your home through air. However, air is not required for radio transmissions.

Mechanical Waves
Wave motion can be studied using a slinky. A slinky is a coil formed with a steel
wire. Below Figure shows a slinky.
Activity

• Place a slinky on a table as shown below Figure
• Hold one end of the slinky and shake it to left and right on the plane of the table.

Demonstration of the formation of waves using a slinky
You will see a wave propagating through the slinky as shown in the figure.

The wave propagating along this slinky is an example for a wave that needs a medium for propagation. Waves that need a material medium for propagation are known as mechanical waves. Waves formed on water surfaces, sound waves that travel in air, and waves formed on a guitar string when the string is plucked are some examples for mechanical waves.

For the propagation of mechanical waves, the participation of the particles in the medium is essential. Based on the direction of motion of the particles of the medium and the direction of propagation of the wave, mechanical waves can be divided into two categories.
1. Transverse waves

2. Longitudinal waves

Transverse Waves
Activity
Apparatus: A slinky, a few pieces of ribbon.

• Tie pieces of ribbon at several places on the slinky.
• Place the slinky on the table as in above activity and shake it to left and right on the plane of the table.
• Observe how each piece of ribbon moves.

Demonstration of the formation of transverse waves using a slinky
In this case, the wave propagates from the end held by the hand towards the fixed end. You will observe that the wave is travelling in a direction perpendicular to the direction the ribbons are moving. Such waves that propagate in a direction perpendicular to the direction the particles of the medium move are called transverse waves. Therefore, this wave is a transverse wave.

In the water waves generated by disturbing a still water surface by dropping an object such as a pebble, water particles of the medium move up and down within a certain range while the wave travels in a direction perpendicular to that.

We mentioned before that when we disturb a water surface after placing a floating object such as a plastic or rubber ball on the surface, the floating object moves up and down. From the up and down motion of the floating object we can understand that the force exerted on the object by the water particles is vertical. That means the water particles move up and down while the waves spread in a direction perpendicular to this. Therefore, the waves that travel on the water surface are
transverse waves.
Direction of motion of the particles of the medium
As shown above Figure, in a transverse wave, the particles of the medium move in a direction perpendicular to the direction of the wave. Below Figure shows how the cross section of a water wave appears at a given instance. The arrow heads indicate the direction that the water particles are moving at that instance.

Cross section of a water wave
The particles at points A and B have traveled the maximum distance in the upward direction. Such points in a wave are known as crests. The particles at C and D have traveled the maximum distance in the downward direction. Such points of a wave are known as troughs.

As shown below Figure, the waves formed by shaking one end of a string up and down whose other end is tied to a post also belong to the category of transverse waves.
Formation of transverse waves in a string
Longitudinal Waves
Activity
Apparatus: A slinky, a piece of ribbon
Place the slinky on a table and fix one end. Tie a ribbon on one coil and move the free end of the slinky forward and backward as shown below Figure. When the free end is pushed forward, the coils near that end are bunched up. This is called a compression. When the free end is pulled back, the coils will stretched-out. This is called a rarefaction.
Demonstration of the formation of longitudinal waves using a slinky

Compressions are formed when the slinky is pushed forward while rarefactions are formed when the free end is moved backward. As a result of this, a wave propagates along the slinky. By observing the motion of the ribbon you can see the in which direction the parts of the spring move.

If the particles of the medium oscillate parallel to the direction of wave propagation, such waves are known as longitudinal waves. You will observe that the waves formed in the slinky in this activity are longitudinal waves.

Sound a tuning fork and touch one of its two arms with your finger tip. You will sense a small vibration in your finger tip. The reason for this is the alternative contacts and removal of contact of the tuning fork arm with your finger. The back and forth motions in the arms of the tuning fork are known as vibrations. We can hear sounds through the waves generated by such vibrations. Such waves that cause the sensation of hearing are known as sound waves. Sound waves generated in air are another example for longitudinal waves.

Physical quantities associated with wave motion
Waves are disturbances that spread from one point to another. Therefore waves have variations that depend on both time and distance. In the waves that we observe in nature, quite often these variations show complex forms. However, in this lesson we will only consider waves of a very simple form known as sinusoidal waves.

The graph in below Figure shows how the displacement from the central position of a particle taking part in the wave motion varies with time.

For example, at time t0 the displacement of that particle is zero. With time, the displacement of this particle increases and at time t1 it takes a maximum positive value. After that the displacement starts to decrease, becomes zero at time t2 and then increases in the negative diraction. At time t3 it takes a maximum negative value and then becomes zero again at t4 . The motion of the particle from time t0 to t4 is called one oscillation. In addition to the word oscillation, the word vibration is also used to describe such motions. If this motion is slow, it is called an oscillation and if it is fast, it is called a vibration.
Variation of displacement of a single particle, with time

The graph in Figure shows how the displacement from the central position of each particle along the travel path of the wave varies with the distance from the source to each of the particles.

Variation of displacement of particles with the distance from the source,
at a given moment
The shape of a transverse wave that we see in a single moment, like the wave traveling along a string, is the same as the shape of the graph of above Figure showing the variation of the displacement of the particles with the distance from the source at a given instance. Because the particle displacement in longitudinal waves takes place in the same direction as the direction of wave propagation, we can not see the form of the graph in a similar manner as for transverse waves. However, if we somehow measure and plot the variation of the displacement with distance we will obtain a graph like that shown above Figure.

With the help of these graphs we can define some physical quantities associated with waves.

Amplitude of a Wave
The maximum displacement shown by the particles taking part in the wave motion is known as the amplitude of the wave.

Wave length of a Wave
The distance between one particle and the closest next particle taking part in the wave motion having the same state of motion is known as the wavelength (λ) of the wave. As an example, a particle on a trough or a crest of the wave shown in Figure(Variation of displacement of a single particle, with time)  has reached its maximum displacement. A particle on the next trough or crest also has the same state of motion. Therefore, the distance between these two particles, that is the distance between two consecutive troughs or crests is equal to the wavelength.

Period
The time taken by a particle for a complete oscillation is known as the period (T). The time taken by a wave to travel a distance equal to the wavelength is also equal to the period.

Frequency
The number of oscillations carried out by aparticle in a unit time is known as the frequency (f). Frequency is equal to the reciprocal of the period. The unit used to measure the frequency is known as Hertz (Hz) and one Hertz is defined as one oscillation per second.
f =1/T
Speed
A wave travels a distance equal to the wavelength (λ) in a time interval equal to the period (T). Therefore its speed is given by v = λ/ T or v = f λ.

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