Waves and sound 1

The velocity of the sound is inversely proportional to the square root of density i.e.

where, v is the velocity of the sound and

is the density of the medium.

The density of damp air is lesser than the dry air. So, sound travels faster in damp air than in dry air.

2. How are beats produced? What is beat frequency?

Beats are produced when two notes of nearly equal frequencies are sounded together. Beat frequency is the number of intense sounds heard per second. If f₁ and f₂ are the frequencies of two notes then the beat frequency is defined as the difference in these frequencies of two notes i.e.

Beat frequency = f₁ - f₂

3. Explain why solders are ordered to break steps while crossing a bridge?

While crossing a bridge, if soldiers are not ordered to break their steps then the frequency of marching may becomes nearly equal to the natural frequency of the bridge that results in the resonance which cause the bridge to vibrate with its maximum amplitude that deteriorates the elastic limit of the bridge causing elastic fatigue. Which may cause damage of the oscillating system i.e. bridge if the displacement of the bridge exceeds elastic limit. So, to avoid a possible damage of the bridge, soldiers are order to break their steps while crossing a bridge.

4. Why sound made at a distance can be heard distinctly at night than in the day time?

As the intensity of the sound during the night increases which increases the velocity of the sound by the following changes:

1. At night, the amount of carbon dioxide is increased and the velocity of sound is greater in carbon dioxide than in air.

2. During night air contains moisture that reduces the density of air. As the velocity of the sound is inversely proportional to the square root of density. the velocity of the sound during night increases.

3. During the night time, there is absence of the sound absorbing materials like vehicles, peoples etc.

Hence, sound made at a distance can be heard distinctly at night than in the day time.

5. During the filling of an empty vessel with water, the pitch of the sound produced goes on changing. Why?

The vessel can be considered as a closed pipe. The frequency of the sound in a closed pipe depends on the length of the pipe. The fundamental frequency f produced by a closed pipe of length 'l' is given by

As the water is poured in the vessel, the length of the air column goes on decreasing which results in the change of the pitch of the sound during the filling of an empty vessel with water.

6. Which organ pipe produces a better quality of sound: a closed pipe or an open pipe?

An open pipe produces a better quality of sound as the quantity of sound is determined by the number of overtones or harmonics present in the sound. The note of an open organ pipe consists of all harmonics but a closed pipe consist only the odd harmonics. Hence, the quality of note produced by an open pipe is better so, an open pipe produces a better quality of sound.

7. What is change in the fundamental frequency of a tube open at both its ends if half of it is dipped vertically in water?

If the length of the tube be l then the fundamental frequency of an open tube is given as:

where v is the velocity of sound in air.

When half of the tube is dipped in water, the tube now behaves as a closed tube of length

. Now, the fundamental frequency f₁ of the closed pipe is given as

From relations 1 & 2, we observed that the fundamental frequency of a tube open at both its ends does not change when it is half dipped vertically in water.

8. Does sound travels faster in hydrogen or in nitrogen?

The velocity of the sound in the medium gas is given by,

where,

is the ratio of molar heat capacities

P is the pressure of the gas

is the density of the gas.

Above relation shows that at the same pressure, the velocity of sound is inversely proportional to the square root of density of the gas. As the density of hydrogen gas is less than that of the nitrogen gas. So, sound travels faster in hydrogen than in nitrogen.

9. Why are bells made of metals and not of wood?

There is high damping damping of sound waves in the wood but very low damping in the metal. If the damping is less, the sound can travel for a long distances for longer duration and vice-versa. Hence, bells are made of metals and not of wood.

10. Why does an empty vessel sounds much?

When an empty vessel is struck it begins to vibrate. This cause the vibration of the air columns inside the vessel with large amplitude. On the other hand, if the vessel is filled with liquid, the liquid molecule vibrate with smaller amplitude. As the intensity I of the sound is directly proportional to the square of the amplitude A i.e.

As a result, the intensity of sound produced is much higher than that produced by the water molecules. Hence, an empty vessel sounds much.

11. Why is the box of sonometer hollow from inside?

When the vibrating tuning fork is placed on the upper board of the sonometer box, the box and air column inside the box begins to vibrate. This vibration is imparted to wire. When the amplitude of vibration of air column is large then resonance can easily be detected. Hence, in order to detect the resonance, the box of the sonometer is made hollow.

12. Two open pipes of the same length produce sounds of different frequencies if their diameters are different. Why?

The fundamental frequency of an open pipe of length l is given by the relation:

where, v is the velocity of sound in air & d is the diameter of the pipe.

As there is a variation of fundamental frequency if the diameter varies. So, the sound produced will be different if their frequencies are different. Hence, the two open pipes of the same length produce sounds of different frequencies if the diameters are different.

13. The frequency of fundamental note of an open organ pipe is double than for closed pipe of the same length. Why?

At the fundamental mode of vibration, there are a node and antinode in a closed pipe but a note and two antinodes in an open pipe.

FOR CLOSED PIPE:

FOR OPEN PIPE:

So, from relations 1 & 2, the wavelength of the note in an open pipe is half than that of in closed pipe that implies the frequency of fundamental note of an open pipe is double than that for closed pipe.

14. Why is end correction necessary for an organ pipe?

As the air at the open end of a organ pipe is free to move and hence the vibrations at this end of a sounding pipe extend a little into the air outside the pipe. Thus antinodes of the stationary wave inside the pipe is some distance away from the open end of the pipe. So, the end correction is necessary.

15. What is the effect of humidity and pressure on the velocity of sound?

Greater is the moisture in the air, smallest is its density for the constant pressure and temperature. As the velocity of the sound varies inversely to the square root of its density i.e.

where, v is the velocity of the sound in air and

is the density of the air.

So, the velocity of sound in moist air is grater than that in dry air. Hence, as humidity increases velocity of sound also increases and vice versa.

16. How is it one can recognize a friend from his or her voice?

Human voice has a large number of frequencies which are simple multiple of a fundamental frequency or overtones. In the voice of different people, different harmonics are present in different number. So, different people have different voice by which one can easily recognize a friend from his or her voice.

17. Transverse wave motion is possible only in solid medium. Why?

If the medium particles vibrate perpendicular to the direction of propagation of the wave, then such waves are called transverse wave. Liquids and gases do not have elasticity of shape so once disturbed, there is no restoring force to pull back a liquid or a gas. For the propagation of the transverse waves, the medium should have rigidity which can not be fulfill by the mediums like gas and liquid. Hence, transverse wave motion is possible only in solid medium.

18. Why do longitudinal waves easily propagate in gases?

Longitudinal waves are those waves which makes the particles of the medium to vibrate about their mean positions along the direction of propagation of the wave. It is formed of a series of compressions and rarefactions. Compressions and rarefactions can easily formed in gases than other medium. Hence, longitudinal waves propagate easily in gases than other media.

19. Longitudinal waves are also called pressure waves. Why?

Longitudinal waves are those waves which makes the particles of the medium to vibrate about their mean positions along the direction of propagation of the wave. It is formed of a series of compressions and rarefactions. The pressure and density are maximum at compressions and minimum at rarefactions. Hence, longitudinal waves are also called pressure waves.

20. We cannot hear explosions on other planets. Why?

For the propagation of the sound, the material medium is required i.e. the sound does not travel in vacuum. Hence, the other planet lies on the vacuum in space and also they are quite far away from the earth. Hence, the sound of explosion does not propagate as there is absence of the material medium through which the sound propagates. Hence, we cannot hear explosions on the other planets.