A tuning fork of known frequency is held at the open end of a long tube which is dipped into water as shown in the figure. The tuning fork of frequency 165 Hz resonates when air columns have length $l_{1} = 50 \pm 0.5 c m and l_{2} = 150 \pm 0.1 c m .$ If the speed of sound in air is $[330 \pm α (0.99)] m / s$ then the value of $α$ is ________

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Detailed Solution

Let be $l$ is wavelength of sound in air
$l_{1} = \frac{λ}{4} a n d l_{2} = \frac{3 λ}{4}$
$λ = 2 (l_{1} - l_{2})$
$v = f λ = 165 \times 2 (150 - 50) \times 10^{- 2} = 330 m / s$
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$d v = \frac{0.5 + 0.1}{150 - 50} \times 330 = 1.98 m / s$

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