A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now:a)f/2b)fc)2fd)3f/2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Explanation:
When a sound wave travels through a pipe or tube, it reflects back and forth between the two ends, creating standing waves. The frequencies at which standing waves can form in a tube depend on the length of the tube and the speed of sound in the medium inside the tube. The fundamental frequency is the lowest frequency at which a standing wave can form in the tube.

Effect of water on frequency:
When the tube is dipped vertically in water so that half of it is in water, the effective length of the tube changes. The speed of sound in water is greater than the speed of sound in air, so the wavelength of the sound waves in water is shorter than the wavelength of the sound waves in air. When the tube is partly submerged in water, the effective length of the tube is reduced by half, so the frequency of the standing waves in the tube is doubled. However, the frequency of the sound wave in air remains the same.

Calculation:
Let L be the original length of the tube.
The fundamental frequency of the air column is given by:
f = v/2L
where v is the speed of sound in air.

When the tube is partly submerged in water, the effective length of the tube is L/2.
The fundamental frequency of the air column in this case is given by:
f' = v/2(L/2) = v/L

Therefore, the frequency of the standing waves in the air column remains the same and is equal to the original fundamental frequency f.

Answer:
The fundamental frequency of the air-column is f.

Answer

Because is not depended on volume

Answer

As we know, f=v/2l
Now, it will act as one end and one end closed.
So, f₀=v/2l’=v/4½=v/2l=f

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