JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Waves & Sound

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A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to :

(A) $322 ms^{- 1}$
(B) $341 ms^{- 1}$
(C) $335 ms^{- 1}$
(D) $328 ms^{- 1}$ ✓ Correct

Answer: (D)

Solution

For the first resonance in a pipe the effective length is a quarter wavelength,

L + e = \frac{λ}{4}

, with

e

the end correction. For the

512

Hz fork,

4 (11 + e) = \frac{v}{512}

; for the

256

Hz fork,

4 (27 + e) = \frac{v}{256}

. Dividing,

\frac{11 + e}{27 + e} = \frac{256}{512} = \frac{1}{2}

, so

22 + 2 e = 27 + e

and

e = 5

cm. Substituting back,

v = 512 \times 4 (11 + 5) = 512 \times 64 = 32768

cm/s

\approx 328

m/s.

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Waves & Sound

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