Question:

A tuning fork $A$ produces $4$ beats per second with another tuning fork $B$ of frequency $320\, Hz$. On filing one of the prongs of $A, 4$ beats per second are again heard when sounded with the same fork $B$. Then the frequency of the fork $A$ before filing is

Updated On: Aug 15, 2022
  • 328 Hz
  • 316 Hz
  • 324 Hz
  • 320 Hz
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The Correct Option is B

Solution and Explanation

There are 4 beats between $A$ and $B$, therefore the possible frequencies of A are $316 $or $324 $ that is $(320 � 4) \,Hz$ When the prong of A is filed, its frequency becomes greater than the original frequency. If we assume that original frequency of A is 324 then on filing its frequency will be greater then 324. The beats between A and B will be more than 4. But it is given that the beats are again 4, therefore, 324 is not possible. Therefore, required frequency must be 316 Hz. (This is true, because on filing the frequency may increase so as to give 4 beats with B of frequency 320 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