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Question-1

A supersonic jet travels with twice the speed of sound in air. What is the angle of the conical wave front of the shock wave produced by the jet?

Solution:
Let the speed of sound=V

And let the speed of the supersonic jet = Vs


       
 

When the speed of an object becomes more than the speed of sound, a shock wave is produced in the medium, conical in shape, with jet at the apex of the cone. The half of the angle of cone ‘θ’ is given by

sinθ =
θ= sin-1
θ= sin-1    or    θ= 300
Therefore, angle if conical wave=2
θ=2×300=600 .

Question-2

Two loud speakers have been installed at a particular place receives very weak sound. What can be the reason for it? What will happen if the loud speaker is switched off?

Solution:
If the difference in the distance of the loud speakers from the listener is an odd multiple of , then due to destructive interference very feeble sound will be heard. If one loud speaker is switched off, then no interference will take place and the feeble sound of the other speaker will be heard.

Question-3

The sound of distant horses can be heard by applying the ear to the ground, whereas it is not audible if the ear is at a little distance above the ground. Explain why it is so?

Solution:
The density of the ground is much higher when compared to that of air. The loudness of sound depends on the density of the medium. Higher the density of the medium more the intensity of sound. The sound produced by distant horses when transmitted through the ground is louder than through air. Thus by applying our ears to the ground, we can hear this sound. But when the ears are a little bit above the ground, the sound travels through air and is therefore not audible.

Question-4

Why should two sources of sound have nearly equal frequencies for the formation of beats?

Solution:
For the formation of distinct beats, frequencies of two sources of sound should be nearly equal, i.e., difference in frequencies of two sources must be small, say less than 10. The impression of sound heard by our ears persists on our mind for 1/10th of a second. If another sound is heard before (1/10) second passes, the impressions of the two sounds mix up and our mind cannot distinguish between the two.

In order to hear distinct beats, time interval between two successive beats must be greater than 1/10 second. Therefore, frequency of beats must be less than 10,i.e., number of beats/sec, which is equal to difference in frequencies of two sources must be less than 10. Hence the two sources should be of nearly equal frequencies.

Question-5

Bats have no eyes. Still they can ascertain distance, directions nature and size of the obstacle. Explain how?

Solution:
Bats have special type of wings. When they fly, they produce ultrasonic waves. These ultrasonic waves are received by them after reflection. Their ears are so sensitive and trained that they not only get the information of distance of the obstacle but also that of the nature of the reflecting surface.

Question-6

(v) Ultrasonic waves in air produced by a vibrating quartz crystal.

 


Solution:
(i) The wave motion is transverse, because the vibrations of particles (kink) of the spring are at right angles to the direction of propagation of the wave.

(ii) The wave motion is longitudinal, because the molecules of the liquid vibrate to and fro about their mean position along the direction of propagation of the wave.

(iii) The given motion is a combination of longitudinal and transverse waves.

(iv) The wave motion is transverse, because the light waves are electromagnetic waves in which electric and magnetic fields vibrate in the direction at right angle to each other and also to the direction of propagation of the wave.

(v) Ultrasonic waves produced by a quartz crystal in air are longitudinal because the molecules of air vibrate to and fro about their mean positions along the direction of propagation of wave due to vibration of the quartz crystal.

Question-7

When we start filling an empty bucket with water the pitch of the sound produced goes on changing. Why?

Solution:
An empty bucket behaves as a closed organ pipe.

The frequency of fundamental notes produced by it is given by v = v/4l. As the bucket starts filling, the length (l) of the resonating air column decreases and hence, frequency, increases. Since pitch of sound depends upon the frequency therefore it changes with the change in the frequency.

Question-8

When a source of sound passes up, whether it is a car horn or train whistle, the pitch we hear goes from high to low. Explain why?

Solution:
When a source of sound, e.g. car horn or a train whistle passes us, the observed pitch varies from high to low. This is due to Doppler’s effect. Initially, the source, e.g., the car horn or a train whistle is approaching us i.e. The source is approaching the observer at rest. Then the observed pitch appears to be more than the true pitch, because v=v

When the source of sound has crossed us, (i.e., the source is receding away from the observer), the observed pitch appears to be less than the true pitch,

because v=v

Question-9

Show that the fundamental frequency of an open or gun pipe is twice that of a closed or gun pipe of the same length.

Solution:
Fundamental frequency of an open or gun pipe,

Va=

Fundamental frequency of a closed or gun pipe

Vc=

= 2 or Va = 2 Vc.

Question-10

The beats are not heard, if the difference on frequencies of the two sounding notes is more than 10 why?

Solution:
If beats produced are more than 10 per second, then due to persistence of hearing, the rise and fall in intensity of sound cannot be made out.

Question-11

Why is it not possible to have interference between the waves produced by violins?

Solution:
This is because the sounds produced will not have a constant phase relationship.

Question-12

A flute has several holes in it. Explain why?

Solution:
A flute is an open organ pipe. It has several holes because the length of the air column can be changed by closing the holes with the fingers so that different frequencies can be produced.

Question-13

Two loud speakers have been installed at a particular place where it receives very weak sound. Give reason. What will happen if one loud speaker is kept off?

Solution:
If the difference in the distance of the loud speakers from the listener is an odd multiple of λ/2, then due to destructive inference, very feeble sound will be heard. If one loud speaker is put off, then no interference will take place and the sound of the other speaker will only be heard.

Question-14

The sound of distant horses can be heard by applying the ear to the ground whereas it is not audible if the ear is little distance above the ground. Explain why it is so?

Solution:
The density of ground is much higher when compared to that of air. The loudness of sound depends upon the density of the medium. Higher is the density of medium more is the intensity of sound. The sound produced by distant horses is louder when it is transmitted through ground than the sound, which is transmitted through air. Thus by applying our ears to the ground, we can hear this sound louder. But when the ears are little bit above the ground, the sound travels through air losing some of its energy to the surroundings and is therefore not audible.

Question-15

Why should two sources of sound have nearly equal frequencies for the formation of beats?

Solution:
For the formation of distinct beats, frequencies of two sources of sound should be nearly equal i.e., difference in frequencies of two sources must be small, say less than 10. The impression of sound heard by our ears persists on our mind for 1/10 th of a second. If another sound is heard before (1/10) second passes, the impressions of the two sounds mix up and our mind cannot distinguish between the two.

In order to heat distinct beats, time interval between two successive beats must be greater then 1/10 second. Therefore, frequency of bests must be less than 10, i.e., number of beats/sec, which is equal to difference in frequencies of two sources must be less than 10. Hence the two sources should be of nearly equal frequencies.

Question-16

Why is a tuning fork made with two prongs? Would a tuning fork be of any use, if one the prongs is cut off?

Solution:
When a tuning fork is set into vibrations, its two prongs move in opposite phase and the center of gravity of the two prongs always remains at the middle point, where the handle joins the two prongs. Therefore a tuning fork having two prongs can be set into vibrations by holding the handle. While it vibrates, its centre of gravity always remains at the same point and on external force is required to maintain the vibrations.

If one of the prongs is cut off, then the centre of gravity of the other prong will change during vibrations. If we hold the tuning fork in our hand, then it will not vibrate but it can oscillate. Hence an external force is required for the tuning fork whose prong was cut off.

Question-17

Bats have no eyes still then it can ascertain the distance, direction, nature and size of the obstacle. Explain why?

Solution:
Bats have special type of wings. When they fly, they produce ultrasonic waves. These ultrasonic waves are received by them after reflection. Their ears are so sensitive and trained that they not only get the information of distance of the obstacle but also the nature of the reflecting surface.

Question-18

When we start filling an empty bucket with water the pitch of the sound produced goes on changing. Why?

Solution:
An empty bucket behaves as a closed organ pipe. The frequency of fundamental note produced by it is given by v = v/4l. As the bucket starts filling, the length (l) of the resonating air column decreases and hence frequency increases. Since pitch of sound depends upon the frequency, it changes with the change in frequency.

Question-19

The fundamental frequency of an open organ pipe is 500 Hz. What will be the fundamental frequency if one end is closed?

Solution:
The frequency of fundamental note of an open pipe is

v0 = v/2l = 500Hz.

Now if one end is closed, then it becomes a closed pipe.

The frequency of the fundamental note emitted by closed pipe is

Vc =
.





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