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Two tuning forks A and B are sounded together and 8 beats/s are heard. A is in resonance with a column of air 32 cm long in a pipe closed at one end and B is similarly in resonance when the length of the column is increased by one cm. Calculate the frequencies of two forks are

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$256 Hz, 264 Hz$

$756 Hz, 748 Hz$

$856 Hz, 848 Hz$

$956 Hz, 948 Hz$

answer is A.

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Detailed Solution

$n_{A} - n_{B} = 8$
Also $n_{A} = \frac{V}{4 (0.32)}, n_{B} = \frac{V}{4 (0.33)}$
$\frac{V}{4 (0.32)} - \frac{V}{4 (0.33)} = 8$
$V = 338 m / s$
$∴ n_{A} = \frac{V}{4 \times 0.32} = \frac{338}{4 \times 0.32} = 264 H z$
$n_{B} = n_{A} - 8 = 256 H z$

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