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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
The frequency of a stretched uniform wire under tension is in resonance with the fundamental frequency of a closed tube. If the tension in the wire is increased by $8 N,$ it is in resonance with the first overtone of the closed tube. The initial tension in the wire is .... $N$
  • ✓
    $1$
  • B
    $4$
  • C
    $8$
  • D
    $16$
✓

Answer

Correct option: A.
$1$
a
(a) According to problem

$\frac{1}{{2L}}\sqrt {\frac{T}{m}} = \frac{v}{{4L}}$…..$(i) $

and $\frac{1}{{2L}}\sqrt {\frac{{T + 8}}{m}} = \frac{{3v}}{{4L}}$ ..…$(ii)$ 

Dividing equation $(i)$ and $(ii),$ $\sqrt {\frac{T}{{T + 8}}} = \frac{1}{3} \Rightarrow T = 1N$

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