A sonometer wire is vibrating at frequency fo I... - JAMB Physics 2000 Question
A sonometer wire is vibrating at frequency fo. If the tension in the wire is doubted 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
correct option: d
For a vibrating sonometer wire, the frequency
F = l/2l √(T/m)
and if the length, l and mass per unit length, m, are constant, then Fo ∝ √T => FoK√T or Fo/√T = K
=> F1o/√F1 = F2o/√F2
∴ F1o/√T1 = F2o/√T2
=
∴F2 = Fo x √2 = Fox√2
F = l/2l √(T/m)
and if the length, l and mass per unit length, m, are constant, then Fo ∝ √T => FoK√T or Fo/√T = K
=> F1o/√F1 = F2o/√F2
∴ F1o/√T1 = F2o/√T2
| thus F2 = | F3x√(2T1 |
| __√T1 |
=
| = | Fox√2 x √T1 |
| √T1 |
∴F2 = Fo x √2 = Fox√2
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