JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Waves & Sound

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In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

(A) $335 m / s$
(B) $370 m / s$
(C) $340 m / s$
(D) $360 m / s$ ✓ Correct

Answer: (D)

Solution

Each air column closed at one end sounds its fundamental at

f = \frac{v}{4 ℓ}

, and the beat rate is the difference of the two fundamentals,

\frac{v}{4} (\frac{1}{ℓ _{1}} - \frac{1}{ℓ _{2}})

. With

ℓ_{1} = 1 m

and

ℓ_{2} = 1.2 m

this is

\frac{v}{4} (1 - \frac{1}{1.2}) = \frac{v}{24}

. Setting it equal to

15 Hz

, the speed of sound in the air column is

360 m/s

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Single correct option

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