Notes On Resonance - ICSE Class 10 Physics


If a body, like a tuning fork is excited with the help of a rubber hammer and left to itself, it executes  vibrations, which are called natural vibrations or free vibrations. Here, the frequency of the vibrating body is referred to as the natural frequency of vibration or just natural frequency.

In the absence of any frictional forces, the amplitude of the tuning fork’s oscillations remains constant.



Dampmed Oscillations


The periodic vibrations of a body with decreasing amplitude are called damped oscillations. In damped oscillations, as the amplitude decreases, there is a decrease in the mechanical energy of the system.

The mechanical energy is lost in doing work against the forces that retard the motion, and is lost or dissipated in the surrounding medium. The frictional forces that retard the motion are called damping forces.

A body can also be excited by applying an external periodic force. For example, when a tuning fork is excited and touch a table top, the table top also vibrates.  The tuning fork is the external periodic force, and the table top vibrates under its influence. The vibrations executed by the table top are known as “forced vibrations.” The table top vibrates with a frequency equal to the external periodic force, that is, the frequency of the tuning fork.


The table vibrates with decreasing amplitude. The vibrations of the table top are spread over a large area. Hence, the vibrating table top comes into contact with a greater number of air particles than the vibrating tuning fork. As a result, a louder sound is produced by the  vibrating table top than by the vibrating tuning fork. 

Thus, in forced vibrations, when a body vibrates under the influence of an external periodic force, it does not vibrate with its natural frequency, but with the natural frequency of the external periodic force.
In the case of free vibrations, the force is applied and then withdrawn. On the other hand, in the case of the forced vibrations, the force is applied repeatedly at regular intervals, so that energy is supplied to the body being forced to vibrate.


Resonance

Consider three pendulums  A, B and C  suspended from a common horizontal rubber cord. Since they are of different lengths, their natural frequencies are also different.

When pendulum A is pulled aside and released, it starts oscillating. Under its influence, B and C also start oscillating with a frequency equal to the natural frequency of A. Hence, B and C execute forced vibrations under the influence of A.

Add one more pendulum, D, of the same length as that of A to this system. When pendulum A is set into oscillations again, B, C and D start oscillating under the influence of A.

Observe that D is oscillating with an increasing amplitude. This is because the natural frequency of D matches with that of A. The vibrations executed by D are a special type of forced vibrations, called resonant vibrations.
When a body vibrates under the influence of an external periodic force whose natural frequency is equal to its own natural frequency, it executes vibrations of increasing amplitude. This phenomenon is called resonance.
During resonance, maximum transfer of energy takes place, and hence, the body executes vibrations of increasing amplitude.

A swing can be kept swinging by periodically timed pushes. The amplitude of the oscillations remains constant if the energy imparted by the push is equal to the energy lost by the system due to the damping forces.
If the frequency of the external periodic force, i.e., the frequency of the the push, is equal to the natural frequency of the swing, then the swing oscillates with increasing amplitude, that is, it exhibits resonance.


Example for Resonance

Two tuning forks A and B of the same natural frequency are mounted on the top of two separate sound boxes such that their open ends face each other. When tuning fork A is set into vibration, the air column in its sound box starts vibrating due to forced vibrations.

These vibrations get transmitted to the air column of the sound box of fork B. As the frequency of these vibrations is the same as that of the natural frequency of B, they are picked up by B, which now starts vibrating with increasing amplitude. Thus, B exhibits resonance.


The resonance apparatus contains a long narrow cylindrical tube ‘A’ connected to a reservoir ‘R’ of water through a rubber tube ‘T’.

Tube A contains a graduated scale that helps to take measurements. The water level in tube ‘A’ can be adjusted by adjusting the position of reservoir ‘R’.

The water in A is brought to the brim by adjusting reservoir R. A tuning fork is brought near the open end of A and excited.

By adjusting reservoir R, the water level in A is slightly lowered to create an air column  AC. The  vibrations of the tuning fork cause the air in column AC to vibrate, and a feeble sound is produced.

The level of water in A is lowered further to increase the length of the air column. The excited tuning fork is held near the open end of A again. A feeble sound is heard again due to the vibration of the air in column AC.
As we repeat the procedure by gradually lowering the water level in A, at a particular water level, a large booming sound is heard. This large booming sound is due to resonance between the frequency of the tuning fork and the frequency of the vibrating air column.

If the water level is lowered still further and the same tuning fork is excited and held near the open end, then another booming sound is heard when the length of air column is nearly three times that of the length of the air column when the first booming sound was heard.


Resonance can also be observed in machine parts. For example, the piston of an engine moves in and out at a particular frequency. The vibrations of the piston are picked up by all the parts of the vehicle. If the natural frequency of the vibration of any part is equal to the frequency of the piston, then it exhibits resonance and vibrates with a large amplitude. The part rattles a lot, the loudest among all the shaking parts, and may even drop out. The rattling stops when the vehicle’s speed is changed. Stringed musical instruments like the guitar and the sitar have a large hollow box, called the sound box. The sound box is so constructed that The frequency of the vibrating air column in it is in resonance with the frequency of the strings.


When the string of a musical instrument is plucked, the vibrations are picked up by the air column inside the sound box.

The air column exhibits resonant vibrations and vibrates with a large amplitude. Since the sound
box has a large area, a large volume of air is set into resonant vibration, and hence, a loud sound
is heard.

Resonance can make a suspension bridge collapse. If the frequency of the steps of soldiers marching on the bridge matches with the frequency of the suspension bridge, then the bridge would exhibit  resonance. The amplitude of the vibrations of the bridge would go on increasing, and the structure would break. That is why soldiers marching over a suspension bridge are told to break their step.

When you tune the receiver of a radio or a television set, you are actually adjusting the frequency of the vibrations produced by the inbuilt electrical circuit, so that it is in resonance with that of the carrier electromagnetic waves coming in from a transmitter. Due to resonance, maximum energy is absorbed from the incoming carrier waves, and you can hear a clear sound and see a clear picture.

Summary


If a body, like a tuning fork is excited with the help of a rubber hammer and left to itself, it executes  vibrations, which are called natural vibrations or free vibrations. Here, the frequency of the vibrating body is referred to as the natural frequency of vibration or just natural frequency.

In the absence of any frictional forces, the amplitude of the tuning fork’s oscillations remains constant.



Dampmed Oscillations


The periodic vibrations of a body with decreasing amplitude are called damped oscillations. In damped oscillations, as the amplitude decreases, there is a decrease in the mechanical energy of the system.

The mechanical energy is lost in doing work against the forces that retard the motion, and is lost or dissipated in the surrounding medium. The frictional forces that retard the motion are called damping forces.

A body can also be excited by applying an external periodic force. For example, when a tuning fork is excited and touch a table top, the table top also vibrates.  The tuning fork is the external periodic force, and the table top vibrates under its influence. The vibrations executed by the table top are known as “forced vibrations.” The table top vibrates with a frequency equal to the external periodic force, that is, the frequency of the tuning fork.


The table vibrates with decreasing amplitude. The vibrations of the table top are spread over a large area. Hence, the vibrating table top comes into contact with a greater number of air particles than the vibrating tuning fork. As a result, a louder sound is produced by the  vibrating table top than by the vibrating tuning fork. 

Thus, in forced vibrations, when a body vibrates under the influence of an external periodic force, it does not vibrate with its natural frequency, but with the natural frequency of the external periodic force.
In the case of free vibrations, the force is applied and then withdrawn. On the other hand, in the case of the forced vibrations, the force is applied repeatedly at regular intervals, so that energy is supplied to the body being forced to vibrate.


Resonance

Consider three pendulums  A, B and C  suspended from a common horizontal rubber cord. Since they are of different lengths, their natural frequencies are also different.

When pendulum A is pulled aside and released, it starts oscillating. Under its influence, B and C also start oscillating with a frequency equal to the natural frequency of A. Hence, B and C execute forced vibrations under the influence of A.

Add one more pendulum, D, of the same length as that of A to this system. When pendulum A is set into oscillations again, B, C and D start oscillating under the influence of A.

Observe that D is oscillating with an increasing amplitude. This is because the natural frequency of D matches with that of A. The vibrations executed by D are a special type of forced vibrations, called resonant vibrations.
When a body vibrates under the influence of an external periodic force whose natural frequency is equal to its own natural frequency, it executes vibrations of increasing amplitude. This phenomenon is called resonance.
During resonance, maximum transfer of energy takes place, and hence, the body executes vibrations of increasing amplitude.

A swing can be kept swinging by periodically timed pushes. The amplitude of the oscillations remains constant if the energy imparted by the push is equal to the energy lost by the system due to the damping forces.
If the frequency of the external periodic force, i.e., the frequency of the the push, is equal to the natural frequency of the swing, then the swing oscillates with increasing amplitude, that is, it exhibits resonance.


Example for Resonance

Two tuning forks A and B of the same natural frequency are mounted on the top of two separate sound boxes such that their open ends face each other. When tuning fork A is set into vibration, the air column in its sound box starts vibrating due to forced vibrations.

These vibrations get transmitted to the air column of the sound box of fork B. As the frequency of these vibrations is the same as that of the natural frequency of B, they are picked up by B, which now starts vibrating with increasing amplitude. Thus, B exhibits resonance.


The resonance apparatus contains a long narrow cylindrical tube ‘A’ connected to a reservoir ‘R’ of water through a rubber tube ‘T’.

Tube A contains a graduated scale that helps to take measurements. The water level in tube ‘A’ can be adjusted by adjusting the position of reservoir ‘R’.

The water in A is brought to the brim by adjusting reservoir R. A tuning fork is brought near the open end of A and excited.

By adjusting reservoir R, the water level in A is slightly lowered to create an air column  AC. The  vibrations of the tuning fork cause the air in column AC to vibrate, and a feeble sound is produced.

The level of water in A is lowered further to increase the length of the air column. The excited tuning fork is held near the open end of A again. A feeble sound is heard again due to the vibration of the air in column AC.
As we repeat the procedure by gradually lowering the water level in A, at a particular water level, a large booming sound is heard. This large booming sound is due to resonance between the frequency of the tuning fork and the frequency of the vibrating air column.

If the water level is lowered still further and the same tuning fork is excited and held near the open end, then another booming sound is heard when the length of air column is nearly three times that of the length of the air column when the first booming sound was heard.


Resonance can also be observed in machine parts. For example, the piston of an engine moves in and out at a particular frequency. The vibrations of the piston are picked up by all the parts of the vehicle. If the natural frequency of the vibration of any part is equal to the frequency of the piston, then it exhibits resonance and vibrates with a large amplitude. The part rattles a lot, the loudest among all the shaking parts, and may even drop out. The rattling stops when the vehicle’s speed is changed. Stringed musical instruments like the guitar and the sitar have a large hollow box, called the sound box. The sound box is so constructed that The frequency of the vibrating air column in it is in resonance with the frequency of the strings.


When the string of a musical instrument is plucked, the vibrations are picked up by the air column inside the sound box.

The air column exhibits resonant vibrations and vibrates with a large amplitude. Since the sound
box has a large area, a large volume of air is set into resonant vibration, and hence, a loud sound
is heard.

Resonance can make a suspension bridge collapse. If the frequency of the steps of soldiers marching on the bridge matches with the frequency of the suspension bridge, then the bridge would exhibit  resonance. The amplitude of the vibrations of the bridge would go on increasing, and the structure would break. That is why soldiers marching over a suspension bridge are told to break their step.

When you tune the receiver of a radio or a television set, you are actually adjusting the frequency of the vibrations produced by the inbuilt electrical circuit, so that it is in resonance with that of the carrier electromagnetic waves coming in from a transmitter. Due to resonance, maximum energy is absorbed from the incoming carrier waves, and you can hear a clear sound and see a clear picture.

Videos

Activities



Activity 1

Walter-fendt.de
has created a java applet to undestand the concept of Resonance such that the top of a spring pendulum  is moved to and fro. We can select one of the three diagrams by using the appropriate radio buttons:

  • The elongations of exciter and resonator as functions of time

  • The amplitude of the resonator's oscillation dependent on the exciter's angular frequency

  • The phase difference between the oscillations of exciter and resonator dependent on the exciter's angular frequency


Go to Activity


Activity 2

Phet.colorado.edu has created a java applet to undestand the concept of resonance such that if one of the sprinngs is oscillated others too oscillate and resonate.

Go to Activity

References

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