# Vibrations of Air Column in Pipes

Investigatory Project – I

Vibrations of Air Column in Pipes – I

Aim: To study the factors affecting the resonant length of closed pipes.

Apparatus: Resonance column apparatus, Tuning forks, Rubber hammer, Metre scale etc.

Theory: In closed pipes, an antinode is formed at the open end and a node at the closed end. The distance between a node and the nearest antinode is λ/4. If ‘l’ is the length of the closed pipe, then l = λ/4.

Therefore, λ = 4l

The resonance occurs when the frequency of the tuning fork equals the frequency of natural vibrations of the closed pipe. Let v is the velocity of sound through air and n is the frequency of the tuning fork, then at resonance,

n = v/ λ = v/4l  or

l = v/4n

The velocity of sound is a constant at constant temperature.

Therefore, l 1/n or resonance length varies inversely with the frequency of the tuning fork.

Procedure:

Set the resonance column apparatus for experiment. Length of the air column is kept very small. A tuning fork of known frequency n, is excited and held horizontally near the mouth of the inner tube. The length of air column is measured. This is repeated again and the average length of the air column is determined. The experiment is repeated for tuning forks of different frequencies and the results are tabulated.

Observations and Calculations

Room temperature in the beginning = ____°C

Room temperature at the end = ____°C

 Frequency of the tuning fork (Hz) First resonating length Mean resonance length (cm) 1 (cm) 2 (cm)

Report:

At constant temperature the resonance length of closed pipes decreases with the increase in frequency of the driving source.

Investigatory Project – II

Vibrations of Air Column in Pipes – 2

Aim: To study the factors affecting the resonant length of closed pipe.

Apparatus: Resonance column apparatus, Tuning fork, Rubber hammer, Metre scale etc.

Theory: The wavelength (λ) corresponding to first resonating (l) is given by,

λ/4 = l +e, where end correction e = 0.3D, D is the inner diameter of the pipe.

The velocity of sound at room temperature (t) is v(t) = 4n(l+e) where n is the frequency of the tuning fork. At constant temperature, velocity of sound is a constant.

l 1/n

For constant n, λ is constant

Therefore, resonating length l (first resonating length observed) varies with diameter of the pipe.

Procedure:

Set the resonance column apparatus for experiment. Length of the air column is kept very small. A tuning fork of known frequency n, is excited and held horizontally over the mouth of the inner tube. The length of air column in the inner tube is slowly increased by raising the tube till a booming sound is heard. The length of the air column is measured. This is repeated again and the average length of the air column is determined. The experiment is repeated for pipes of different inner diameters.

Observations and Calculations

Frequency of the tuning fork, n = ___ Hz

Room temperature, t = ___°C

To study the vibration of resonating length with inner diameter of the pipe

 Trial No: Inner diameter of tube D (cm) First resonating length, l (cm) 1 2 3 4 5

Report:

The resonating length of closed pipe with its inner diameter at constant temperature is studied.