Question:

A tuning fork arrangement (pair) produces $4$ beats/s with one fork of frequency $288\, cps$. A little wax is placed on the unknown fork and it then produces $2$ beats/s. The frequency of the unknown fork is :

Updated On: Jul 2, 2022
  • $286\, cps$
  • $292\, cps$
  • $294\, cps$
  • $288\, cps$
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The Correct Option is B

Solution and Explanation

The tuning fork of frequency $288 Hz$ is producing 4 beats/s with the unknown tuning fork i. e., the frequency difference between them is 4 .Therefore, the frequency of unknown tuning fork $=288 \pm 4=292$ or $284$ On placing a little wax on unknown tuning fork, its frequency decreases but now the number of beats produced per second is 2 i.e., the frequency difference now decreases. It is possible only when before placing the wax, the frequency of unknown fork is greater than the frequency of given tuning fork. Hence, the frequency of unknown tuning fork $=292 Hz$
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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