Contents
Physics Topics cover a broad range of concepts that are essential to understanding the natural world.
What is the Speed of Sound ?
Sound takes some time to travel from the sound producing body to our ears. The speed of sound depends on the nature of medium (or material) through which it travels. The speed of sound is different in different materials. In general, sound travels slowest in gases, faster in liquids and fastest in solids. The speeds of sound in air (a gas), water (a liquid) and iron or steel (a solid) are given below :
From the above table we can see that the speed of sound in air is 340 metres per second (which is written in short as 340 m/s). This means that sound travels a distance of 340 metres in 1 second through air. Sound travels faster in water than through air. For example, the speed of sound in water is 1500 metres per second. Thus, sound travels about 5 times faster in water than in air. This means that sound can be heard very fast inside water. The fact that sound can be heard very fast inside water is used by creatures like dolphins and whales living in the sea-water to communicate with one another (even when they are far away).
Sound travels faster in solids than in liquids. For example, sound travels at a speed of 5000 metres per second through iron (or steel). This is more than 3 times the speed of sound in water. Here is an interesting consequence of the very high speed of sound in iron or steel. If a train is very far away from us, we cannot hear the sound of approaching train through the air. But if we put our ear to the railway line made of steel, then we can hear the sound of the coming train easily even if it is quite far away. This is due to the fact that sound travels much more faster through the railway line made of steel than through air.
In fact, sound travels about 15 times faster in steel than in air. So, if we want to hear a train approaching from far away, it is more convenient to put the ear to the railway track (railway line) because the sound of train travels much more faster through solid railway track made of steel than through air. Since wood is a solid and air is a gas, so sound travels faster in wood than in air. Again, wood is a solid and water is a liquid, so sound travels faster in wood than in water. We will now compare the speeds of sound and light.
Sound Travels Slower Than Light
The speed of sound in air is about 340 m/s and the speed of light in air is 300,000,000 m/s. This means that sound travels at a slow speed but light travels much, much faster than sound. In fact, the speed of light is very great as compared to the speed of sound. So, though sound may take a few seconds to travel a distance of a few hundred metres, light will take practically no time to reach a distance of even a few kilometres. We will now give an observation from our everyday life which is based on the low speed of sound in air but very high speed of light. It is a common observation that in the rainy season, the flash of lightning is seen first and the sound of thunder is heard a little later (though both are produced at the same time in clouds) (see Figure). It is due to the very high speed of light that we see the flash of lightning first and it is due to comparatively low speed of sound that the thunder is heard a little later. We will now describe the organ of hearing sound called ear’.
We Hear Through Our Ears
The ears are the sense organs which help us in hearing sound. So, we hear through our ears. We will now describe the construction and working of a human ear briefly. A highly simplified diagram of human ear is shown in Figure.
The shape of the outer part of ear (which we see outside the head) is like a funnel. The outer part of ear is called ‘pinna’ and it is attached to about 2 to 3 centimetre long passage called ‘ear canal’. At the end of ear canal a thin, elastic and circular membrane called ‘eardrum’ is stretched tightly (see Figure 8). There are three small and delicate bones called hammer, anvil and stirrup in the middle part of the ear which are linked to one another. One end of hammer touches the eardrum and its other end is connected to second bone anvil.
The other end of anvil is connected to third bone called stirrup. And the free end of stirrup touches the membrane over the oval window (see Figure). The inner part of ear has a coiled tube called ‘cochlea’. One end of cochlea is connected to middle part of ear through the elastic membrane over the oval window. Cochlea is filled with a liquid. The liquid present in cochlea contains nerve cells which are sensitive to sound.
The other end of cochlea is connected to auditory nerve which goes into the brain (see Figure). Please note that the three tiny bones in the middle part of ear act as a system of levers and amplify sound vibrations coming from the eardrum before passing them on to the inner part of the ear (cochlea).
We will now describe the working of ear. The sound waves (coming from a sound producing body) are collected by the pinna of outer part of ear. These sound waves pass through the ear canal and fall on the eardrum. When the sound waves fall on the eardrum, the eardrum starts vibrating back and forth rapidly. The vibrating eardrum causes a small bone hammer to vibrate. From hammer, vibrations are passed on to second bone ‘anvil’ and then to the third bone ‘stirrup’.
The vibrating stirrup strikes on the membrane of oval window and passes the amplified vibrations to the liquid in cochlea. Due to this, liquid in cochlea begins to vibrate. The vibrating liquid of cochlea sets up electrical impulses in the nerve cells present in it. These electrical impulses are carried by auditory nerve to the brain (see Figure). The brain interprets these electrical impulses as sound and we get the sensation of hearing.
Activity 5
We can perform an activity to demonstrate the working of eardrum as follows: Take a plastic tin can and cut its both ends. Stretch a piece of thin rubber sheet (from a burst balloon) across one end of the plastic can and fasten it tightly with a rubber band. Hold the plastic can vertically in your hand with the ‘rubber sheet covered end’ at the top. Put four or five small grains of a cereal (like rice) on the stretched rubber sheet.
Keeping the plastic can vertical, ask your friend to shout ‘hurray, hurray’, upwards from the open end (lower end) of the plastic can by bringing his mouth below it. We will observe that when the sounds of hurray, hurray fall on the stretched rubber sheet from below, the rice grains placed over it start jumping up and down. The up and down movement of rice grains placed on the stretched rubber sheet tells us that when sound waves fall on it from below the stretched rubber sheet starts vibrating (up and down). This is how the eardrum in our ear works.
We should not put anything (like pin, pencil or pen, etc.) inside our ears. This is because they can tear the eardrum. The tearing of eardrum can make a person deaf. Our ears are very delicate organs. We should take proper care of our ears and protect them from damage.
Amplitude, Time-Period And Frequency Of A Vibration
We have all seen a swing (or jhoola) in the children’s park. If we displace the lower end of a swing to one side and then release it, the swing starts moving ‘backwards and forwards’ repeatedly. Though the top end of swing remains fixed at the same position but the lower end of swing (on which we sit), keeps on moving backwards and forwards, again and again (The alternate ‘backwards and forwards’ motion is also called ‘back and forth’ motion or ‘to-and-fro’ motion). The motion of a swing is actually an example of vibrations or oscillations.
We can now say that: A repeated ‘back and forth’ motion is called vibrations (or oscillations). When an object moves back and forth continuously, we say that it is making vibrations (or oscillations). For example, when a swing moves back and forth repeatedly, we say that the swing is making vibrations (or oscillations). Please note that whether we use the word vibrations or oscillations, it will mean the same thing. We will now give the example of a simple pendulum to understand the meaning of vibrations (or oscillations) more clearly.
A simple pendulum can be made by tying about one metre long thread from a small metal ball and suspending it from a height as shown in Figure (a). The small metal ball of pendulum is called bob. When the pendulum is at rest (not vibrating), then its bob is in the normal position or central position A [see Figure (a)].
If we displace the bob of pendulum to the left side to position B and then release it, it will start vibrating (or oscillating) like a swing between positions B and C [see Figure (b)]. The bob first goes from position B to position C, and then comes back to B. It again goes from position B to position C, and then comes back to B. This motion of the pendulum bob is repeated again and again. We say that the
pendulum bob is vibrating (or oscillating) between positions B and C. In Figure 9(b), the position A of bob is called central position and the positions B and C are called the extreme positions of the bob. When the pendulum bob goes from one extreme position B to the other extreme position C, and then comes back to B, we say that it completes one vibration (or one oscillation). Every vibration (or oscillation) has three characteristics: amplitude, time-period, and frequency. These are discussed below.
1. Amplitude of Vibrations
When a simple pendulum vibrates, its bob goes to equal distances on either side of its central position. For example, in Figure (b), the pendulum bob goes to equal distances AB and AC from its central position. The maximum distance to which the bob of a vibrating pendulum goes from its central position is called amplitude of vibrations (or amplitude of oscillations). In Figure (b), the distance AB is the amplitude of vibration of this simple pendulum. Since the distance AB is equal to distance AC, so we can also say that distance AC is the amplitude of vibration of this pendulum.
From this discussion we conclude that: The maximum displacement of a vibrating object from its central position is called the amplitude of vibrations. In other words, the maximum displacement of an oscillating object from its central position is called amplitude of oscillations. The amplitude actually tells us how far the vibrating object is displaced from its central position. We can increase the amplitude of vibrations of a simple pendulum by raising the height from which the pendulum bob is initially released. Similarly, we can decrease the amplitude of vibrations by releasing the pendulum bob from a smaller height.
2. Time-Period of Vibrations
One complete to-and-fro movement of the pendulum bob is called one vibration (or one oscillation). The time taken by pendulum bob to complete one vibration (or one oscillation) is called the time-period of pendulum. For example, in Figure 9(b), the time taken by the pendulum bob to travel from position B to position C, and back to B, will be the time-period of this pendulum. In general, we can say that: The time taken by a vibrating object to complete one vibration is called its time-period. In other words, the time taken by an oscillating object to complete one oscillation is called its time-period. The unit of measuring time-period is ‘second’.
The time taken by one vibration (or one oscillation) of a simple pendulum is very short and hence cannot be measured accurately. So, to find the time taken by one vibration (or time-period), we measure the time taken by a large number of vibrations. Dividing the ‘total time’ by the ‘total number of vibrations’, we get the time for one vibration (or time-period) of the pendulum. For example, we can measure the time for, say 20 vibrations of the pendulum by using a stop watch.
Now, dividing this ‘time’ by ‘20’ will give us the time taken by one vibration. That is, it will give us the time-period (of vibration) of pendulum. For a given pendulum, the time- period is the same every time. The time-period of a pendulum depends only on the length of pendulum. It does not depend on amplitude of vibrations.
3. Frequency of Vibrations
The number of vibrations made per second by a vibrating body is called the frequency of vibration. ‘Per second’ means in ‘one second’. So, we can also say that: The number of vibrations made in one second is called the frequency of vibration. In other words, the number of oscillations made in one second is called the frequency of oscillations. The unit of frequency of vibrations (or oscillations) of a vibrating object is hertz. That is, frequency is measured in hertz (which is written in short form as Hz). When an object makes 1 vibration per second (or 1 oscillation per second), its frequency is said to be I hertz. And if an object makes 10 vibrations per second, then its frequency will be 10 hertz. The frequency actually tells us how fast the vibrating object repeats its motion. We can increase the frequency of a simple pendulum by reducing the length of its thread. And we can decrease the frequency of a simple pendulum by increasing the length of its thread.
To find the frequency of a simple pendulum, we measure the time taken by the pendulum to make a large number of vibrations. Dividing the ‘number of vibrations’ by the ‘time taken’ we get the number of vibrations made in one second. This will give us the frequency of the pendulum. For example, we can measure the time for, say 20 vibrations of the pendulum by using a stop watch. Now, dividing ‘20’ by the ‘time taken’ will give us the number of vibrations made in one second. This will be the frequency of the pendulum. The calculation of frequency of a pendulum will become more clear from the following example.
Example Problem.
A pendulum makes 15 oscillations in 5 seconds. What is the frequency of the pendulum ?
Solution.
The number of oscillations made by a pendulum in 1 second is called its frequency. Now :
In 5 seconds, pendulum makes = 15 oscillations
So, In 1 second, pendulum makes = \(\frac{15}{5}\) oscillations
= 3 oscillations
Thus, the frequency of this pendulum is 3 oscillations per second or 3 hertz.
Please note that the frequency of vibrations (or oscillations) of a simple pendulum is very low. So, a vibrating simple pendulum produces a sound having very low frequency. And the very low frequency sound produced by a vibrating simple pendulum cannot be heard by our ears. An object must vibrate at a frequency of at least 20 hertz to be able to produce audible sound (which can be heard by our ears). We will now give the relation between time-period and frequency.
Relation between Time-Period and Frequency
We have just studied that ‘time-period is the time required to make 1 vibration’ and ‘frequency is the number of vibrations made in 1 second’. This means that time-period is equal to the reciprocal (or inverse) of frequency. That is:
Time-period \(=\frac{1}{\text { Frequency }}\)
This is the relation between the ‘Time-period’ and ‘Frequency’ of vibrations (or oscillations). We will now use this relation to solve a numerical problem.
Example Problem.
What is the time-period of a pendulum which is vibrating with a frequency of 10 hertz ?
Solution.
We know that: Time-period \(=\frac{1}{\text { Frequency }}\)
= \(\frac{1}{10}\)
= 0.1 second
Thus, the time-period of this pendulum is 0.1 second.