Question

if l₁ and l₂ are the lengths of air column for two air column for two consecutiveresonance position when a tuning fork of frequency f is sounded in a resonancetube, then end correction is :

Answer 1

End correction in a resonance tube experiment can be calculated as half the difference between the lengths of the air column at two consecutive resonances, which corresponds to half a wavelength of the sound.

This can be expressed as (l₂ - l₁)/2.

Step-by-step explanation:

The question pertains to the calculation of end correction in a resonance tube experiment involving two consecutive resonance positions of an air column.

When a tuning fork of frequency f is used with a resonant air column, the lengths of the air column l₁ and l₂ at the first and second resonances are related to the wavelength of the sound in the tube.

End correction is a small additional length that compensates for the air disturbance at the open end of the tube that does not fit into the idealized theoretical model.

Step-by-step explanation:

1. For a tube open at both ends, the resonant frequencies correspond to the fundamental frequency f₁ and its overtones.
2. The formula relating frequency, wavelength, and speed of sound is f = v/λ, where f is the frequency, λ is the wavelength, and v is the speed of sound.
3. The length of the air column at the first resonance, l₁, is approximately equal to half of the wavelength of the sound (λ/2), and at the second resonance, l₂, it is approximately equal to one full wavelength (λ).
4. To find the end correction, we consider the difference in length between two consecutive resonance positions. This difference corresponds to half a wavelength (λ/2).
5. Therefore, end correction is half the difference between l₂ and l₁, which can be calculated as (l₂ - l₁)/2.