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Q.

Two tuning forks A and B give 5 beats/s. A resonates with a column of air 15 cm long, closed at one end, and B with a column 30.5 cm long, open at both ends. Neglecting end correction, the frequencies of A and B are respectively

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a

295 Hz, 300 Hz

b

300 Hz, 305 Hz

c

305 Hz, 300 Hz

d

305, 295 Hz

answer is C.

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Detailed Solution

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$\frac{v}{4 \times 15} - \frac{v}{2 \times 30.5} = 5 \Rightarrow \frac{v}{60} - \frac{v}{61} = 5$
$\Rightarrow v = 5 \times 60 \times 61 cm / s$

$n_{1} = \frac{5 \times 60 \times 61}{60} = 305 Hz$

$n_{2} = \frac{5 \times 60 \times 61}{61} = 300 Hz$

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Two tuning forks A and B give 5 beats/s. A resonates with a column of air 15 cm long, closed at one end, and B with a column 30.5 cm long, open at both ends. Neglecting end correction, the frequencies of A and B are respectively