Two tuning forks A and B produce 8 beats/s when sounded together.… - Vidyadip

MCQ

Two tuning forks $A$ and $B$ produce $8\ beats/s$ when sounded together. A gas column $37.5\ cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5\ cm$ of the same gas in a similar pipe is required for a similar resonance with fork $B$. The frequencies of these two tuning forks, are

✓
$308\ Hz , 300\ Hz$
B
$208\ Hz , 200\ Hz$
C
$300\ Hz , 400\ Hz$
D
$350\ Hz , 500\ Hz$

✓

Answer

Correct option: A.

$308\ Hz , 300\ Hz$

a
For tuning fork $'A'\frac{{{\lambda _1}}}{4} = 37.5$

so $n_{1}=\frac{v}{\lambda_{1}}=\frac{v}{4 \times 37.5}$

For tuning fork $'B'$ $\frac{\lambda_{2}}{4}=38.5$

$\therefore n_{2}=\frac{v}{\lambda_{2}}=\frac{v}{4 \times 38.5}$

$\therefore n_{1}-n_{2}=8 \Rightarrow \frac{v}{4 \times 37.5}-\frac{v}{4 \times 38.5}=8$

$\therefore v=(8 \times 4 \times 37.5 \times 38.5)$

$n_{1}=\frac{8 \times 4 \times 37.5 \times 38.5}{4 \times 37.5}=308 \mathrm{\,Hz}$

and $n_{2}=308-8=300 \mathrm{\,Hz}$

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