Q76 / 90 · JEE Main 2014 (19 Apr Online) · Physics

The total length of a sonometer wire fixed between two bridges is 110 cm. Now, two more bridges are placed to divide the length of the wire in the ratio 6:3:2. If the tension in the wire is 400 N and the mass per unit length of the wire is 0.01 kg m-1, then the minimum common frequency with which all the three parts can vibrate, is

  • Correct answer
    A
    1000Hz
  • B
    1100Hz
  • C
    100Hz
  • D
    110Hz

Solution

l 1 : l 2 : l 3    = 6:3:2

The frequancy in any nth mode for a segment is f=nv2l=constant

no of loops ∝ length of the segment

so, no of loops are in the ratio 6:3:2

hence total loops =11

The string is divided in 60 cm, 30 cm, & 20 cm part such that for minimum frequency, the wavelength is maximum

λ2=111x110=10cm

f = V λ = 1 λ · F μ = 1 0.2 4 0 0 0.01 = 1 0 0 0 Hz

Hence, the correct answer is option: 'A'.

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