When an object which execute vibration motion is slightly displaced from its stable position and is left then due to the effect of restitution force it vibrates with its natural (fundamental) frequency. This type of vibration is called the “free vibration”. In ideal free vibration the amplitude of the object is constant state of But in reality when the object excutes free vibrations then it experiences some frictional force in the medium in which it is vibrating. As a result some part of its energy is lost as heat. Hence, the amplitude of the object decreases with time. Those types of vibrations whose amplitude decreases with time are called the “damped vibrations.”
If somehow we can provide the same energy to the vibrating object as to which it has lost; then the object keeps on vibrating with the same (constant) amplitude. This type of vibration is called the “maintained vibrations”.
A vibrating object forces another object (which has the tendency to vibrate) to vibrate. It is also possible if their fundamental frequencies are different. This type of vibration is called the “forced vibrations”. This type of vibrations end very soon because in this situation the second vibrating object does not vibrate with its fundamental frequency but vibrates with the frequency of the first vibrating object.
When the frequency of first vibrating object is equal to the fundamental frequency of the second vibrating object then the amplitude of forced vibrations increases relatively. This is called the “resonance”. Every impulse of frequency force helps the system state to vibrate. Due to this the amplitude of the system keeps on increasing.
Resonance tube is that device with the help of which the state of resonance is produced by vibrating the air column and then calculating the velocity of sound in air.
Fig: Resonance tube
As shown in figure resonance tube has a one meter long glass tube T of 5 cm diameter. It is joined at the lower end by a rubber tube with the liquid (water) vessel (R). The vessel (R) is placed on a vertical stand on which it can be moved up and down and can be positioned. Tube T is filled with water so that normally its 2/3 part is filled with water. There is an air column in the tube T from the level of water to its mouth. Hence, this tube works as a closed organ pipe. Here, with the help of vessel R the length of air column can be changed. Therefore, its vibration frequency can be changed.
When a vibrating tuning fork is brought close to the open end of a tube T. Then forced vibrations are produced in the air column. Now if by changing the length of the air column, its fundamental frequency is kept same as tuning fork’s frequency, then the amplitude of vibration is maximum; which is called the state of resonance and hence high intensity sound (shrill) is heard. In this situation the length of the air column is calculated. This is called the resonant length. This process is repeated again and again and the minimum (smallest) resonant length is calculated. This is called the first resonant length, at this time the air column vibrates with its fundamental frequency. If first resonant length is l then according to the figure(a).
(a) First phase of resonance
(b) Second of resonance
