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Difference between the resonance lengths of two successive overtones of a tube closed at one end was 32 cm.If the end correction of the tube is 0.5 cm, what is the resonance length of the pipe when it vibrates at it’sfundamental frequency?

Question

Difference between the resonance lengths of two successive overtones of a tube closed at one end was 32 cm.If the end correction of the tube is 0.5 cm, what is the resonance length of the pipe when it vibrates at it’sfundamental frequency?

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Solution

The difference in resonance lengths of two successive overtones in a tube closed at one end is equivalent to one wavelength (λ).

Given that this difference is 32 cm, we can say that λ = 32 cm.

The fundamental frequency (also known as the first harmonic) of a tube closed at one end is equivalent to a quarter of the wavelength.

So, the resonance length (L) of the tube at its fundamental frequency is λ/4.

Therefore, L = λ/4 = 32 cm / 4 = 8 cm.

However, we also need to account for the end correction. The end correction is a small additional length at the open end of the tube where the air vibrates slightly beyond the physical end of the tube.

Given that the end correction is 0.5 cm, we add this to our calculated resonance length.

So, the total resonance length of the tube when it vibrates at its fundamental frequency is L + end correction = 8 cm + 0.5 cm = 8.5 cm.

This problem has been solved

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