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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
Two sitar strings, $A$  and $B,$  playing the note $'Dha'$  are slightly out of tune and produce beats and frequency  $5\,Hz.$  The tension of the string $B$ is slightly increased and the beat frequency is found to decrease by  $3\,Hz$ . If the frequency of $A$ is $425\,Hz,$  the original frequency of $B$ is  ... $Hz$
  • A
    $430$
  • B
    $428$
  • C
    $422$
  • ✓
    $420$
✓

Answer

Correct option: D.
$420$
d
$\mathrm{n}_{\mathrm{A}}=425 \mathrm{Hz}, \mathrm{n}_{\mathrm{B}}=?$

Beat frequency $x=5$ $Hz$ which is decreasing $(5 \rightarrow 3)$ after increasing the tension of the string $B$.

Also tension of string $\mathrm{B}$ increasing so

$\mathrm{n}_{\mathrm{B}} \uparrow(\because \mathrm{n} \propto \sqrt{\mathrm{T}})$

Hence $\quad \mathrm{n}_{\mathrm{A}}-\mathrm{n}_{\mathrm{B}} \uparrow=x \downarrow \longrightarrow$ correct

$\mathrm{n}_{\mathrm{B}} \uparrow-\mathrm{n}_{\mathrm{A}}=\mathrm{x} \downarrow  \longrightarrow \text { incorrect }$

$\therefore \mathrm{n}_{\mathrm{B}}=\mathrm{n}_{\mathrm{A}}-\mathrm{x}=425-5=420 \mathrm{Hz}$

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