physics

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The length of a sonometer wire AB is 100cm
where should the two bridges be placed from A to divide the wire in 3 segments whose fundamental frequencies are in the ratio of 1:2:6
options:
1.60cm,90cm
2.40cm,80cm

  • physics -

    Let L1, L2, L3 be the lengths of three segments. Then L1+L2+L3 = 100.
    Also from the laws of vibrations of stretched string
    f1•L1=f2•L2=f3•L3

    Given
    f1:f2:f3 = 1:2:6.
    Therefore,
    L2 =L1/2, L3 =L1/6.
    L1 + L1/2 + L1/6 = 100,
    10•L1/6 = 100.
    L1 = 60cm. L2 = L1/2 = 30 cm, L3 =L1/6 = 10 cm.
    The first bridge - L1 = 60 cm
    The second bridge – L1+l2 = 90 cm

    Answer: 1.60cm,90cm

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