Physics RESONANCE

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RESONANCE

Resonance

The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the oscillator is called `text(resonance)`.

In our daily life we encounter phenomena which involve resonance. Your experience with swings is a good example of resonance. You might have realized that the skill in swinging to greater heights lies in the synchronization of the rhythm of pushing against the ground with the natural frequency of the swing.

To illustrate this point further, let us consider a set of five simple pendulums of assorted lengths suspended from a common rope as shown in Fig. The pendulums 1 and 4 have the same lengths and the others have different lengths. Now let us set pendulum 1 into motion. The energy from this pendulum gets transferred to other pendulums through the connecting rope and they start oscillating. The driving force is provided through the connecting rope. The frequency of this force is the frequency with which pendulum 1 oscillates. If we observe the response of pendulums 2, 3 and 5, they first start oscillating with their natural frequencies of oscillations and different amplitudes, but this motion is gradually damped and not sustained. Their frequencies of oscillation gradually change and ultimately they oscillate with the frequency of pendulum 1, i.e. the frequency of the driving force but with different amplitudes. They oscillate with small amplitudes. The response of pendulum 4 is in contrast to this set of pendulums. It oscillates with the same frequency as that of pendulum 1 and its amplitude gradually picks up and becomes very large. A resonance-like response is seen. This happens because in this the condition for resonance is satisfied, i.e. the natural frequency of the system coincides with that of the driving force.

The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the oscillator is called `text(resonance)`.

In our daily life we encounter phenomena which involve resonance. Your experience with swings is a good example of resonance. You might have realized that the skill in swinging to greater heights lies in the synchronization of the rhythm of pushing against the ground with the natural frequency of the swing.

To illustrate this point further, let us consider a set of five simple pendulums of assorted lengths suspended from a common rope as shown in Fig. The pendulums 1 and 4 have the same lengths and the others have different lengths. Now let us set pendulum 1 into motion. The energy from this pendulum gets transferred to other pendulums through the connecting rope and they start oscillating. The driving force is provided through the connecting rope. The frequency of this force is the frequency with which pendulum 1 oscillates. If we observe the response of pendulums 2, 3 and 5, they first start oscillating with their natural frequencies of oscillations and different amplitudes, but this motion is gradually damped and not sustained. Their frequencies of oscillation gradually change and ultimately they oscillate with the frequency of pendulum 1, i.e. the frequency of the driving force but with different amplitudes. They oscillate with small amplitudes. The response of pendulum 4 is in contrast to this set of pendulums. It oscillates with the same frequency as that of pendulum 1 and its amplitude gradually picks up and becomes very large. A resonance-like response is seen. This happens because in this the condition for resonance is satisfied, i.e. the natural frequency of the system coincides with that of the driving force.

Resonance tube

It is used to find experimentally the velocity of sound in air.

In this tube, water is filled level of which can be varied. The surface of water can betaken as closed end to the sound wave in air.

When a tuning fork is vibrated and placed above the open end of the tube vertically. One of this wave travel through air column and reflects from surface of water. The superposition of incident and reflected wave causes formation of standing waves for selected lengths of air column called resonating lengths as shown.

If `l_1` is the first resonance length, then applying end correction, the vibrating length is `l_1 + e`

So, `(lamda)/4=l_1+e`

And if second resonance length is `l_2`, then applying end correction, the second vibrating length is `l_2 + e`

So `(3lamda)/4=l_2 + 4`

`:.lamda/2=l_2-l_1` `=>` `lamda=2(lamda_2-lamda_1)`

Since the air columns in the two cases are in resonance with the tuning fork, i.e. are vibrating with the frequency of the tuning fork. So,

`v=flamda=fxx2(l_2 - l_1)`

`v=2f(l_2 -l_1)`

It is used to find experimentally the velocity of sound in air.

In this tube, water is filled level of which can be varied. The surface of water can betaken as closed end to the sound wave in air.

When a tuning fork is vibrated and placed above the open end of the tube vertically. One of this wave travel through air column and reflects from surface of water. The superposition of incident and reflected wave causes formation of standing waves for selected lengths of air column called resonating lengths as shown.

If `l_1` is the first resonance length, then applying end correction, the vibrating length is `l_1 + e`

So, `(lamda)/4=l_1+e`

And if second resonance length is `l_2`, then applying end correction, the second vibrating length is `l_2 + e`

So `(3lamda)/4=l_2 + 4`

`:.lamda/2=l_2-l_1` `=>` `lamda=2(lamda_2-lamda_1)`

Since the air columns in the two cases are in resonance with the tuning fork, i.e. are vibrating with the frequency of the tuning fork. So,

`v=flamda=fxx2(l_2 - l_1)`

`v=2f(l_2 -l_1)`

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