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A tuning fork A of frequency 370 Hz gives 6 beats in 2 seconds when sounded with another tuning fork B. What could be the frequency of B?

A tuning fork A of frequency 370 Hz gives 6 beats in 2 seconds when sounded with another tuning fork B. What could be the frequency of B? Correct Answer 373 Hz

CONCEPT:

  • We consider two sine waves of equal amplitudes and directions. The different frequencies and wavelengths of the waves are considered here while the wave speeds are the same.
  • Beat frequency: The difference in frequency of two sound sources sounding together is called beat frequency. 
    • The beat frequency is produced when two waves of different frequencies superimpose when they travel in the same path with the same wave speed.

Let a source have frequency f1 and the other source has frequency f2 then the beat frequency is given by:

Beat frequency (f) = |f1 – f2|

CALCULATION:

The frequency of beats is f1 - f2

  • In the question there are 6 beats in two seconds which shows frequency is 3 Hz.
  • The frequency of the tuning fork B is either 3 Hz more or 3 Hz less than the frequency of A. Thus, it could be either 367 Hz or 373 Hz. In the option only 373 Hz is the option (3).
  • For beats to be audible the difference in frequencies should not be very large. An average human ear cannot distinguish the variation of intensity if the variation is 16 times per second.

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