Question:

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

Updated On: Jul 5, 2022
  • $2f$
  • $\frac{3}{4}f$
  • $\frac{f}{2}$
  • $f$
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The Correct Option is D

Solution and Explanation

For cylindrical tube, open at both ends, fundamental frequency is $f = \frac{v}{2L} \quad ...(i)$ where $v$ is the speed of the sound in air and $L$ is the length of the tube.
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When half of its length dipped vertically in water, then it will become a closed tube with half the length of the air column, so its fundamental frequency is $f' = \frac{v}{4\left(\frac{L}{2} \right)} =\frac{v}{2L} = f$ (Using $(i)$) i.e. the frequency remains unchanged,
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Concepts Used:

Waves

Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.

Types of Waves:

Transverse Waves -

Waves in which the medium moves at right angles to the direction of the wave.

Examples of transverse waves:

  • Water waves (ripples of gravity waves, not sound through water)
  • Light waves
  • S-wave earthquake waves
  • Stringed instruments
  • Torsion wave

The high point of a transverse wave is a crest. The low part is a trough.

Longitudinal Wave -

A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.

Examples of longitudinal waves:

  • Sound waves
  • P-type earthquake waves
  • Compression wave