Contents
Physics Topics can also be used to explain the behavior of complex systems, such as the stock market or the dynamics of traffic flow.
What are the Resonance Types of Vibration? What is the Difference Between Resonance and Forced Vibration?
Usually, when a body executes a forced vibration, its amplitude and velocity remains small. In most cases, the frequency of the applied periodic force does not come close to the natural frequency of the vibrating body. However, when the frequency of the body, the amplitude and the velocity of the body become very large. This phenomenon is called resonance.
It is important to keep in mind that some objects are very resonant at a particular frequency while others barely resonate. For example, a temple bell will only ring at a fixed frequency, which is its resonant frequency; but a lump of jelly will vibrate at many different frequencies but will not resonate at all.
Definition: When the frequency of the applied periodic force matches the natural frequency of a vibrating body, its amplitude rapidly increases to a large value. This phenomenon is called resonance.
This vibration is also known as sympathetic vibration.
Resonant vibration is of two types.
Amplitude resonance: In this case, the amplitude of vibration becomes maximum. At amplitude resonance the frequency of applied force is slightly less than the natural frequency i.e., ω = \(\sqrt{\omega_0^2-2 b^2}\).
Velocity resonance: In this case, the velocity of the vibrating body becomes maximum. Velocity resonance occurs when the natural frequency is exactly equal to the frequency of applied force i.e., ω = ω0.
Example of resonance:
i) A thread is tied loosely between P and Q, and four simple pendulums C, D, E, F are suspended from the thread [Fig.].
Pendulums C and D have the same length. So they have the same natural frequency. But the lengths of pendulums E and F are different from those of C and D. So they have different natural frequencies. Now if pendulum C is set into vibration, it executes SHM. Hence, a periodic force acts on the pendulums D, E, F through amplitudes and velocities of vibration are not large; but pendulum D vibrates with a large amplitude. This is because pendulum D resonates with pendulum C.
As soon as pendulum D is set into resonant vibration, it applies, in turn, periodic forces on pendulums C, E and F through the thread PQ. This does not affect the vibrations of E and F very much, but pendulum C experiences resonance. In this way, energy is alternately transferred from C to D and D to C. As a result, it is observed that, when the amplitude of vibration of pendulum C becomes very large, pendulum D almost comes to a stop; in the next moment the amplitude of pendulum D starts to increase while that of pendulum C gradually decreases.
ii) Resonant air column: The length of an air column contained in a tube determines the natural frequency of the column. If a vibrating tuning fork is held at the mouth of such a tube, forced vibration is set up in the air column. If the frequency of the tuning fork is the same as the natural frequency of the air column, then resonance occurs in the air column and a loud sound is heard. Using this phenomenon, sometimes a tuning fork is mounted on a hollow box. The box is so shaped that its frequency becomes equal to the natural frequency of the tuning fork. So, when the tuning fork is struck a resonance is produced and a loud sound is heard.
iii) Hollow box in musical instruments: In musical instruments, such as violin, esraj, sitar, etc., the strings are stretched on a wooden hollow box or cavity. The vibration of a string induces forced vibration on the wooden box and on a large mass of air inside it. This increases the intensity of the emitted sound. If resonance occurs the emitted sound is further intensified.
iv) In musical instruments like violin, esraj, sitar, etc., there are a number of strings in addition to the principal string, which are adjusted or tuned to predefined notes of different frequencies. When the principal string is played to produce a certain note, resonant vibrations may occur in some other string. This contributes to the increase in both the loudness and quality of the musical sound.
v) Helmholtz’s resonator: To detect the presence of tones of different frequencies in a note, the German scientist Helmholtz devised a resonator. It consists of a brass shell of nearly spherical shape with two openings a and b of different diameters [Fig.]. The natural frequency of the air inside the spherical shell depends on the size of the shell. The larger opening a, called hole or neck, is turned towards the source of sound while we place our ears in front of the smaller opening b, called pip. Now, suppose that in a note there is a tone whose frequency is equal to the natural frequency of the resonator. In that case, resonance is produced in the air inside the resonator and the tone will be heard distinctly. With the help of different resonators of known frequencies, we can detect different tones in a note.
Comparison between Forced Vibration and Resonance
| Forced Vibration | Resonance |
| 1. The body vibrates with the frequency of the applied periodic force instead of its own natural frequency. | 1. Resonance is also a forced vibration. In this case, the natural frequency of the body becomes equal to the frequency of the applied periodic force. |
| 2. The amplitude of the forced vibration is generally very small. | 2. In resonance, the amplitude of vibration is very large. In the absence of resistive forces, the amplitude of vibration approaches infinity. |
| 3. In a forced vibration, the body at first tries to vibrate with its natural frequency. But after some time natural vibration stops and the body vibrates with the frequency of the applied periodic force. | 3. In resonance, a vibrating body does not lose its natural frequency. Here the natural frequency of the body is equal to the frequency of the applied periodic force. |