A tuning fork of known frequency is held at the open end of a long tube, which is dipped into water as shown. The tuning fork of frequency 165 Hz resonates with air column, when air column is vibrating in 1st and 3rd harmonic with air column lengths $l_{1}$ = (50 ± 0.5) cm and $l_{2}$ = (150 ± 0.1) cm respectively. The speed of sound in air column is

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(320 ± 0.99) m/s

(330 ± 0.99) m/s

(330 ± 1.98) m/s

(320 ± 1.98) m/s

answer is B.

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Detailed Solution

$l_{1} = \frac{λ}{4}, l_{2} = \frac{3}{4} λ \Rightarrow λ = 2 (l_{2} - l_{1}), v = n λ = 330 m / s, a l s o \frac{d v}{v} = \frac{d l_{2} + d l_{1}}{l_{2} - l_{1}}, d v = 1.98 m / s .$

= nl = 330 m/s, also , dv = 1.98 m/s.

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