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…
JEE Main 2014 — Physics Waves & Oscillations
2014mcqhard
The total length of a sonometer wire fixed between two bridges is 110cm. 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 400N and the mass per unit length of the wire is 0.01kgm−1, then the minimum common frequency with which all the three parts can vibrate, is
Official previous-year question
Held on 19 Apr 2014 · Verified 6 Jul 2026.
Options
A
1000Hz
B
1100Hz
C
100Hz
D
110Hz
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Solution
l1:l2:l3=6:3:2
The frequancy in any nth mode for a segment is f=2lnv=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
2λ=111x110=10cm
f=λV=λ1⋅μF=0.210.01400=1000Hz
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