Physics-
General
Easy

Question

Two vibrating tuning forks produce progressive waves given by y subscript 1 end subscript equals 4 sin invisible function application 500 pi t a n d y subscript 2 end subscript equals sin invisible function application 50 pi t. Number of beats produced per minute is

  1. 360    
  2. 180    
  3. 3    
  4. 60    

The correct answer is: 180


    Given,
    y subscript 1 end subscript equals 4 sin invisible function application 500 pi t horizontal ellipsis.. open parentheses i close parentheses
    y subscript 2 end subscript equals 2 sin invisible function application 506 blank pi t blank horizontal ellipsis.. open parentheses i i close parentheses
    Comparing Eqs. (i) and (ii)
    Y=a sin ωt……………(iii)
    We have,
    omega subscript 1 end subscript equals 500 pi
    ⟹ f subscript 1 end subscript fraction numerator 500 pi over denominator 2 pi end fraction equals 250 b e a t s divided by s
    And
    omega subscript 2 end subscript equals 506 pi
    ⟹ f subscript 22 end subscript equals fraction numerator 506 pi over denominator 2 pi end fraction equals 253 blank b e a t s divided by s
    Thus, number of beats produced
    equals f subscript 2 end subscript minus f subscript 1 end subscript equals 253 minus 250
    =3 beats/s
    =3×60 beats/min
    =180 beats/min

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