A sonometer wire is vibrating at frequency fo. If the tension in the wire is doubled while the length and the mass per unit length are kept constant, the new frequency of vibration is
A
fo/2
B
2fo
C
fo/√2
D
fo√2
Verified Correct Answer: D.
Physical Principles & Numerical Solution
For a vibrating sonometer wire, the frequency
F = l/2l \sqrt(T/m)
and if the length, l and mass per unit length, m, are constant, then Fo ∝ \sqrtT => FoK\sqrtT or Fo/\sqrtT = K
=> F1o/\sqrtF1 = F2o/\sqrtF2
∴ F1o/\sqrtT1 = F2o/\sqrtT2
thus F2 =
F3x\sqrt(2T1
__\sqrtT1
=
=
Fox\sqrt2 x \sqrtT1
\sqrtT1
∴F2 = Fo x \sqrt2 = Fox\sqrt2
Source: Myschool Past Questions Archive (Record #11277)