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The study of Physics Topics involves the exploration of matter, energy, and the forces that govern the universe.
How do you Prove Sound Travels in the Form of Waves?
The sensation felt by our ears is called sound. Sound is a form of energy. Sound is that form of energy which makes us hear. We hear many sounds around us in our everyday life. At home we hear the sounds of our parents talking to us.
We also hear the sounds of telephone bell, radio, television, stereo-system, mixer-grinder and washing machine. At school we hear the sounds of our teachers, classmates and the school bell. We hear the sounds of scooters, motorcycles, cars, buses and trucks on the road.
And the sound of a flying aeroplane is heard from the sky. At a music concert, we hear the sounds produced by various musical instruments like sitar, veena, violin, guitar, tanpura, piano, harmonium, flute, shehnai, tabla and cymbals, etc. And in a garden, we hear the sounds of chirping of birds.
A wave is a vibratory disturbance in a medium which carries energy from one point to another without there being a direct contact between the two points. A wave is produced by the vibrations of the particles of the medium through which it passes.
When a wave passes through a medium, the medium itself does not move along the direction of the wave, only the particles of the medium vibrate about their fixed positions. For example, when sound waves produced by a ringing bell come to us through air, there is no actual movement of the air from the bell to our ears. Only the sound energy travels through the vibrations of the air molecules.
Similarly, when a water wave passes over the surface of water in a pond, it does not drive water to one side of the pond, only the water molecules vibrate up and down about their fixed positions. There are two types of waves : longitudinal waves and transverse waves.
Sound Waves are Longitudinal Waves
A wave in which the particles of the medium vibrate back and forth in the ‘same direction’ in which the wave is moving, is called a longitudinal wave. A longitudinal wave has been illustrated in Figure. In Figure, the direction of wave has been shown from A to B, in the horizontal plane.
The direction of vibrations of the particles is also along AB, parallel to the direction of wave. That is, the particles of the medium vibrate back and forth in the horizontal direction. Please note that longitudinal waves can be produced in all the three media: solids, liquids and gases. We will now describe the formation of longitudinal waves on a spring or slinky. A long, flexible spring which can be compressed or extended easily is called slinky.
1. The waves which travel along a spring (or slinky) when it is pushed and pulled at one end, are longitudinal waves. Before we discuss this further, it is necessary to understand the words ‘compression’ and ‘rarefaction’ as applied to a spring. The normal position of a spring has been shown in Figure (a).
(a) In a spring, a compression is that part in which the coils (or turns) are closer together than normal. In Figure (b), the regions marked C are compressions.
(b) In a spring, a rarefaction is that part in which the coils (or turns) are farther apart than normal. In Figure (b), the regions marked R are rarefactions.
We will now describe how longitudinal waves are formed on a spring. Figure (a) shows the normal position of a spring whose one end is fixed. Now, if the free end of the spring is moved to and fro continuously, then longitudinal waves consisting of alternate compressions and rarefactions travel along the spring [see Figure (b)].
When a wave travels along the spring, then each turn of the spring moves back and forth by only a small distance in the direction of the wave. Since the particles of the medium (turns of the spring) are moving back and forth in the direction of the wave, the waves which travel across the spring are longitudinal waves.
2. The sound waves in air are longitudinal waves. When a sound wave passes through air, the particles of air vibrate back and forth parallel to the direction of sound wave. Thus, when a sound wave travels in the horizontal direction, then the particles of the medium also vibrate back and forth in the horizontal direction. Please note that the waves produced in air when a guitar wire (sitar wire, tanpura wire or violin wire) is plucked are longitudinal waves, because they are sound waves.
We know that when a longitudinal wave travels in a medium, then the particles of the medium vibrate back and forth in the same direction in which the wave travels. When the vibrating particles come closer to one another than they normally are, then there is a momentary reduction in volume and a compression is formed.
On the other hand, when the vibrating particles move farther apart from one another than they normally are, then there is a momentary increase in volume and a rarefaction is formed.
A compression is that part of a longitudinal wave in which the particles of the medium are closer to one another than they normally are, and there is a momentary reduction in volume of the medium. Figure 6 shows a longitudinal sound wave in air. In Figure, all the regions marked C are compressions.
A rarefaction is that part of a longitudinal wave in which the particles of the medium are farther apart than normal, and there is a momentary increase in the volume of the medium. In Figure, all the regions marked R are rarefactions.
Another point to be noted is that in a compression, there is a temporary increase in the density of the medium; and in a rarefaction, there is a temporary decrease in the density of the medium through which a longitudinal wave passes.
When the density of the medium increases, its pressure also increases; and when the density of the medium decreases, then its pressure also decreases. So, we can also say that compression is a region of high pressure whereas rarefaction is a region of low pressure. From the above discussion we conclude that a longitudinal wave consists of compressions and rarefactions travelling through a medium.
There are also another type of waves called transverse waves. A wave in which the particles of the medium vibrate up and down ‘at right angles’ to the direction in which the wave is moving, is called a transverse wave. A transverse wave is illustrated in Figure.
In Figure, the direction of wave is from P to Q but the vibrations of the particles are along RS which is at right angles to the direction of wave PQ. So, this is a transverse wave. Transverse waves can be produced only in solids and liquids but not in gases. We will now describe the formation of transverse waves on a long spring or slinky.
1. The waves produced by moving one end of a long spring (or slinky) up and down rapidly, whose other end is fixed, are transverse waves. The transverse wave produced on a slinky is shown in Figure.
As the wave passes along the slinky in the horizontal direction, the particles of slinky vibrate ‘up and down’ at right angles to the direction of wave.
2. The water waves (or ripples) formed on the surface of water in a pond are also transverse waves.
This is because of the fact that in a water wave, the molecules of water move up and down in the vertical direction when the wave travels in the horizontal direction along the water surface.
Since the water molecules vibrate up and down at the same place, therefore, a cork or leaf placed on the surface of water moves up and down at the same place as water wave moves across the surface of the pond. The shape of transverse water waves produced on the surface of water is just like those formed on a slinky as shown in Figure.
Thus, when a stone is dropped in a pond of water, transverse water waves are produced on the surface of water. Even the light waves and radio waves are transverse waves.
We know that when a transverse wave travels horizontally in a medium, the particles of the medium vibrate up and down in the vertical direction. When the vibrating particles move upward, above the line of zero disturbance, they form an ‘elevation’ or ‘hump’ and when the vibrating particles move downward, below the line of zero disturbance, they form a ‘depression’ or ‘hollow’ (see Figure).
The ‘elevation’ or ‘hump’ in a transverse wave is called crest. In other words, a crest is that part of the transverse wave which is above the line of zero disturbance of the medium. In Figure, XY is the line of zero disturbance and A and C are the two crests of the transverse water waves.
The ‘depression’ or ‘hollow’ in a transverse wave is called trough. In other words, a trough is that part of the transverse wave which is below the line of zero disturbance. In Figure, B and D are the two troughs of the transverse water waves. These troughs are below the line of zero disturbance XY.
When we look at the water waves moving on the surface of water in a pond, we find that at some places the water level is higher than the normal level whereas at other places the water level is lower than the normal level. The ‘higher water level’ points are ‘crests’ and the Tower water level’ points are ‘troughs’ of the water waves. From the above discussion we conclude that a transverse wave consists of crests and troughs.
When a wave passes through a medium, then some property of the medium like density or displacement etc., changes. So, waves are represented graphically by showing how some property of the medium (like density, displacement, etc.,) changes when a wave passes through it. This point will become more clear from the following discussion.
Graphical Representation of Longitudinal Waves
When a longitudinal wave passes through a medium, say air, then some of the particles of air get crowded together and form compression, whereas other particles go farther apart and form a rarefaction. So, a longitudinal wave is represented pictorially by showing the compressions and rarefactions as follows (see Figure).
In a compression, the density of air is high whereas in a rarefaction, the density of air is low. Thus, when a longitudinal wave passes through air, then the density of air changes continuously. So, a longitudinal wave in air is represented graphically by plotting the density of air against distance from the source. in other words, a longitudinal wave is represented by a density-distance graph. A longitudinal wave in air has been represented by means of a density-distance graph in Figure.
In Figure, the horizontal line XY represents the normal density of air. All the points above this line represent greater density and those below this line represent less density of air than normal. So, here A and C represent compressions whereas B and D represent rarefactions.
Please note that the wavy line in Figure which represents a longitudinal wave in air, actually shows the variation of the density of air as the longitudinal wave passes through it.
We will now describe the graphical representation of transverse waves. When a transverse wave passes through a medium, then some particles of the medium are displaced above the line of zero disturbance whereas others are displaced below the line of zero disturbance.
So, a transverse wave is represented graphically by plotting the displacement of different particles of the medium from the line of zero disturbance against distance from the source. In other words, a transverse wave is represented by a displacement-distance graph.
Figure shows how a transverse wave is represented by a displacement-distance graph. In the above Figure, the horizontal line XY represents the line of zero disturbance of the particles of the medium. All the particles above this line have positive displacements and those below it have negative displacements.
In the above Figure, A and C represent two crests, and B and D represent two troughs of the transverse wave. Thus, the wavy line in Figure which represents a transverse wave actually shows the variation of the displacements of the particles in the different parts of the wave. We will now describe the various characteristics of a sound wave.