Question

In fig. A, B, C and D represent test tubes each of height $20cm$ which are filled with water up to heights of $12cm$ , $14cm$ , $16cm$ and $18cm$ respectively. If a vibrating tuning fork is placed over the mouth of the tube D, a loud sound is heard. Give the reason for your observation in each case.

Answer 1

Here we will use the concept of resonant frequency. Resonance is defined as the phenomenon in which the amplitude is increased, when the frequency of a force applied periodically will be equal to or close to the natural frequency. When the vibrating tuning fork is brought near to tube B, the adjacent tubes will start vibrating and these vibrations will produce a sound.

Complete answer:
In this case, when the tuning fork is brought near the tube D, the adjacent tubes will start vibrating. With the vibration, a resonance will occur with the air column in tube B whereas the resonance will not occur with the air columns in tube A and C.

Now, the length of the air column in tube B is $20 - 14 = 6cm$ and the length of the air column in tube D is $20 - 18 = 2cm$ . As we can see that the length of the air column in tube B is three times the length of the air column in tube D. therefore, the frequency vibration of the air column in tube B will be equal to the frequency vibration of the sir column in tube D. Also, the frequency of the air column in tube A and C will not be equal to the frequency vibration of the air column in tube D.

Therefore, a loud sound will be produced in tube B and the least sound will be produced in the tubes A and C.

Note: Here, the frequency of air columns in tubes A and C will also not be equal to the frequency of the air column in tube B. Also, the frequency at which the response amplitude will be relatively maximum are known as the system's resonant frequency. At this frequency, large amplitude oscillations will be produced by even small periodic driving forces.