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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 transverse vibrations in a stretched string is $200 Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be  .... $Hz$
  • A
    $25$
  • B
    $200$
  • C
    $400 $
  • ✓
    $1600$
✓

Answer

Correct option: D.
$1600$
d
(d) $n = \frac{1}{{2l}}\sqrt {\frac{T}{m}} $

==>$\frac{{{n_1}}}{{{n_2}}} = \frac{{{l_2}}}{{{l_1}}}\sqrt {\frac{{{T_1}}}{{{T_2}}}} $$ = \frac{1}{4}\sqrt {\frac{1}{4}} = \frac{1}{8}$

==> ${n_2} = 8{n_1} = 8 \times 200 = 1600Hz$

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