## Chapter 3.2 - Different Kinds of Vibrations and Characteristics of Sound Exercise 145

Question 1
What do you mean by wave motion?
Solution 1
The propagation of wave through a medium due to the repeated oscillatory motion of the particles of the medium about their mean position, the motion being handed over from one particle of the medium to the next particle progressively is referred to as wave motion.
Question 2
Differentiate between forced vibrations and resonance.
Solution 2
When an oscillatory system is made to oscillate under the action of an externally applied periodic force, it is said to execute forced vibrations. In this case the external frequency may or may not be equal to the natural frequency of the body.
In case of resonance, the externally applied periodic force has the same frequency as the natural frequency of oscillation of the given oscillatory system.

Question 3
Name three factors on which the frequency of vibration of a stretched string depends.
Solution 3
Frequency of vibrations of a stretched string depends upon:
1. Frequency of the fundamental note of a stretched string is inversely proportional to the length of the vibrating string.
2. Frequency is directly proportional to the square root of the tension of the string.
3. Frequency is inversely proportional to the square root of linear density. That is, mass per unit length of the material of the string. Thinner is the wire, higher is the frequency.
Question 4
State any two ways of increasing the frequency of vibration of a stretched string.
Solution 4
Frequency of vibration of a stretched string can be increased by:
1. By increasing the tension in the string.
2. By decreasing the length of the string.

Question 5
When a troop crosses a suspension bridge, the soldiers are asked to break steps. Explain.
Solution 5
When a troop crosses a suspension bridge, the soldiers are asked to break steps. The reason is that when soldiers are in steps, all the separate forces exerted by them are in same phase and therefore vibrations of a particular frequency are produced. Now if the natural frequency of the bridge happens to be equal to the frequency of steps (or an integer multiple of it) the bridge will vibrate with a large amplitude due to resonance and the suspension bridge could crumble.
Question 6
How does the medium affect the amplitude of free vibrations of a body?
Solution 6
The medium offers some resistance due to which the amplitude of vibrations decreases with time.

Question 7
Is pitch same as frequency?
Solution 7
No, pitch is not the same as frequency.
Question 8
What adjustments would you make for turning a stringed instrument for it to emit a note of desired frequency?
Solution 8
We know that the frequency of the string depends on the length, density and tension; hence the tension is changed to bring about the desired tuning because length is fixed in this case.

Question 9
Explain, why strings of different thicknesses are provided on a stringed instrument?
Solution 9
In stringed instruments frequency depends on thickness or radius of string. So to produce different frequencies different strings of different thicknesses are provided.
Question 10
In fig. 14, P, Q, R and S represent test tubes each of height 20 cm which are filled with water upto heights of 10 cm, 14 cm, 16 cm and 18 cm respectively. If a vibrating tuning fork is placed over the mouth of test tube Q, a loud sound is heard.
(i) Describe the observations with the tubes P, R and S.
(ii) Give the reason for your observation in each case.
(iii) State the principle illustrated by the above experiment. Solution 10
(i) No loud sound is heard with P and R but a loud sound is heard with S.
(ii) Resonance occurs with the air column in tubes Q and S whereas no resonance occurs in the air columns of tubes P and R. The frequency of vibrations of air column in the tube S is thrice the frequency of vibrations of air column in the tube Q, while the frequency of vibrations of air column in tubes P and R is neither equal to nor an integer multiple of frequency of vibrations of air column in tube Q.
(iii) When the frequency of vibrations of air column is either equal to or an integer multiple of the frequency of the vibrating tuning fork, resonance occurs.

Question 11
Write two differences between transverse and longitudinal waves.
Solution 11 Question 12
What are free vibrations?
Solution 12
The vibrations of a body with constant amplitude and constant frequency are called free vibrations.

Question 13
What is meant by the natural frequency of vibration of a body?
Solution 13
A body clamped at one point, if disturbed slightly from its position of rest starts vibrating. The vibrations so produced are called natural vibrations of the body. The natural period or frequency of such vibrations is called frequency of vibration of a body. This frequency depends upon the shape and size of the body.
Question 14
What are damped vibrations?
Solution 14
The periodic vibrations of body of decreasing amplitude are called the damped vibrations.

Question 15
Explain the phenomenon of resonance giving examples.
Solution 15
When the frequency of the forced vibration is equal to the natural frequency of a body nearby or an integer multiple of it then the body vibrates with a large amplitude. This phenomenon is called resonance.
E.g.1 all stringed instruments are provided with sound box (or sound chamber). This box is so constructed that the column of of air inside it, has a natural frequency which is the same as that of the strings stretched on it, so that when the strings are made to vibrate, the air column inside the box is set to forced vibrations. Since the sound box has a large area, it sets a large volume of air into vibration of the same frequency as that of the string. So, due to resonance, a loud sound is produced.
E.g.2 Radio and TV receivers have electronic circuits which produce electrical vibrations, the frequency of which can be changed by changing the values of the electrical components of that circuit. When we want to tune a radio or TV receiver, we merely adjust the values of the electronic components to produce vibrations of frequency equal to that of the incoming radio waves which we want to receive. When the two frequencies match, due to resonance, the energy or signal of that particular frequency is received from the incoming waves. The signal is then amplified in the receiver set.
Question 16
Fig. 13 shows three ways in which the string of an instrument can vibrate. (i)    Which of the diagram shows the principle note?
(ii)    Which has the frequency four times that of the first?
(iii)    What is the ratio of the frequency of the vibration in (a) and (b)?
Solution 16
(i) Diagram (a) shows the principal note as the string in this diagram is vibrating in one loop.
(ii) Diagram (c) has the frequency four times that of first.
(iii) The ratio of frequency of the vibration in (a) and (b) is 1:2.

Question 17
Distinguish between music and noise.
Solution 17 Question 18
Give two examples of forced vibrations.
Solution 18
Examples of forced vibrations:
1. When the stem of a vibrating tuning fork is pressed against the top of a table, the tuning fork forces the table top to vibrate with its own frequency. The vibrations produced in the table top are forced vibrations.
2. When a guitar is played, the vibrations produced by the strings of the guitar are the forced vibrations.

## Chapter 3.2 - Different Kinds of Vibrations and Characteristics of Sound Exercise 146

Question 1
With which of the following frequencies does a tuning fork of frequency 256 Hz resonate? 288 Hz, 314 Hz, 333 Hz, 512 Hz.
Solution 1
Frequency 512 Hz is twice the natural frequency of the tuning fork (256 Hz), hence the tuning fork will resonate at the frequency 512 Hz.
Question 2
In fig. 15 shows two tuning forks P and Q of the same frequency mounted on separate sound boxes with their open ends facing each other. The fork A is set into vibration. (i) Describe your observation. (ii) State the principle illustrated by this experiment. Solution 2
(i) If the tuning fork A is set into vibration, the other fork B also starts vibrating and a loud sound is heard.
The vibrating tuning fork A produces the forced vibrations in the air column of its sound box. These vibrations are of large amplitude because of large surface area of the air in the sound box and they are communicated to the sound box of the fork B. The air column of B starts vibrating with the frequency of fork A. Since the frequency of these vibrations is same as the natural frequency of the fork B, the fork B starts vibrating due to resonance.
(ii) The principle of 'resonance' is illustrated by this experiment.
Statement: When the frequency of the forced vibration is equal to the natural frequency of a body nearby or an integer multiple of it then the body vibrates with a large amplitude. This phenomenon is called resonance.

Question 3
In fig. 16 P, Q, R and S are four pendulums suspended from the same elastic string XX'. Lengths of pendulum P and S are equal, while the length of Q is smaller and R is longer. The pendulum P is set into vibration. What is your observation? Give reason for your observation. Solution 3
Observation: It is observed that the pendulum S also starts vibrating and it ultimately acquires the same amplitude as that of P and the vibrations of S are in phase with those of P (i.e. they reach their extreme positions on either side simultaneously). The pendulums Q and R also vibrate but they vibrate with smaller amplitudes.
Reason: The vibrations produced in pendulum P are communicated to the other pendulums Q,R and S through the elastic string XX'. The pendulums Q and R are in the state of forced vibrations, while the pendulum S is in the state of resonance. This is because the natural period of pendulum S is equal to that of P (being of same length), and therefore resonance takes place. The pendulum S therefore vibrates with the amplitude of P and remains in phase with the pendulum A.