Physics-
General
Easy

Question

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is 350 m s to the power of negative 1 end exponent is

  1. 1250 Hz    
  2. 625 Hz    
  3. 417 Hz    
  4. 715 Hz    

The correct answer is: 625 Hz


    In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at lambda divided by 4 and second resonance occurs at 3 lambda divided by 4.
    Thus, at first resonance
    fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses
    And a second resonance
    fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses

    Subtracting Eq.(i) from Eq.(ii), we have
    fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13
    ⟹ fraction numerator lambda over denominator 2 end fraction equals 28
    therefore blank lambda equals 56 blank c m
    Hence, frequency of tuning fork
    v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z

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