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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
Two tuning forks $A$ and $B$ sounded together give $6$ beats per second. With an air resonance tube closed at one end, the two forks give resonance when the two air columns are $24 cm$ and $25 cm$ respectively. Calculate the frequencies of forks.
  • A
    $120\,Hz , 124\,Hz$
  • B
    $110\,Hz ,114\,Hz$
  • ✓
    $150\,Hz , 144\,Hz$
  • D
    $170\,Hz , 118\,Hz$
✓

Answer

Correct option: C.
$150\,Hz , 144\,Hz$
c
(c)

Let the frequency of the first fork be $f_1$ and that of second be $f_2$.

We then have, $f_1=\frac{v}{4 \times 24}$ and

$f _2=\frac{ v }{4 \times 25}$

We also see that $f _1 > f _2$

$\therefore f _1- f _2=6$

$\text { and } \frac{ f _1}{ f _2}=\frac{24}{25}$

Solving $(i)$ and $(ii)$, we get $f _1=150\,Hz$ and $f _2=144\,Hz$

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